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Number and Alphabet Series

49 questions

All types49Multiple choice26Numeric13Fill in the blank10
Question 1Question →

Complete the given number series by identifying the logical pattern.

Fill in the blanks below

In the number series 5,10,20,35,55,…5, 10, 20, 35, 55, \dots, the value of the missing term is .
Show answer & explanation

Answer

80
The terms increase by successive multiples of 5: +5,+10,+15,+20+5, +10, +15, +20. Continuing this pattern, the next increment must be +25+25, giving 55+25=8055 + 25 = 80.

Step-by-Step Solution

1
Calculate the differences between consecutive terms in the series.
10−5=510 - 5 = 5, 20−10=1020 - 10 = 10, 35−20=1535 - 20 = 15, 55−35=2055 - 35 = 20.
Finding the differences between consecutive terms helps identify the underlying sequence rule.
2
Determine the pattern governing the differences.
The differences form a sequence that increases by 55 at each step (5,10,15,20,…5, 10, 15, 20, \dots).
The next difference must be 20+5=2520 + 5 = 25.
3
Add the calculated difference to the preceding term to obtain the missing value.
55+25=8055 + 25 = 80.
Adding the next difference of 2525 to the fifth term (5555) produces the sixth term.

Key Concept

Number Series Completion via Increasing Differences
Question 2Question →

A researcher is cataloging environmental samples using a specific alphabetical labeling sequence. The first five sample labels are assigned as follows:

BKR, EJU, IHY, NED, TAJ

If the labeling system continues with the exact same underlying logic, what will be the exact label for the next sample in the sequence?

Show answer & explanation

Answer: AVQ

Answer

AVQ
The correct sequence combines three distinct rules running in parallel across the three letter positions. The first position moves forward in increasing steps (+3, +4, +5, +6, +7) ending at A. The second position moves backward in increasing steps (-1, -2, -3, -4, -5) ending at V. The third position moves forward in increasing steps (+3, +4, +5, +6, +7) ending at Q. Combining these yields the label AVQ.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term: B, E, I, N, T.
The positional shifts are: B(+3) → E(+4) → I(+5) → N(+6) → T.
This establishes an increasing forward progression for the first position.
2
Calculate the next letter for the first position.
The next shift must be +7. T (20) + 7 = 27. Since the alphabet has 26 letters, 27 corresponds to A (1). The first letter is A.
Applying the established mathematical pattern to find the missing term.
3
Analyze the pattern of the second letter in each term: K, J, H, E, A.
The positional shifts are: K(-1) → J(-2) → H(-3) → E(-4) → A.
This establishes an increasing backward progression for the second position.
4
Calculate the next letter for the second position.
The next shift must be -5. A (1) - 5 = -4. Wrapping around the alphabet backwards (26 - 4) gives 22, which is V. The second letter is V.
Continuing the reverse alphabet indexing accurately.
5
Analyze the pattern of the third letter in each term: R, U, Y, D, J.
The positional shifts are: R(+3) → U(+4) → Y(+5) → D(+6) → J. (Note: Y(25)+5 = 30; 30-26 = 4 which is D).
This establishes an increasing forward progression for the third position.
6
Calculate the next letter for the third position.
The next shift must be +7. J (10) + 7 = 17. The 17th letter is Q. The third letter is Q.
Completing the final position using the deduced logical rule.

Key Concept

Identifying independent progressive positional shift patterns in alphanumeric coding sequences.
Estimated Time:1m 30s
Question 3Question →
Find the next term in the following number sequence: 3,5,8,13,22,39,72,…3, 5, 8, 13, 22, 39, 72, \dots
Show answer & explanation

Answer: 137

Answer

The next number in the given series is 137.
Computing second-level differences between terms reveals a doubling sequence (1,2,4,8,161, 2, 4, 8, 16). The next second-level difference is 3232. Adding 3232 to the last first-level difference (3333) yields 6565. Finally, adding 6565 to the last term (7272) gives the correct value of 137137.

Step-by-Step Solution

1
Compute the first-order differences between consecutive terms in the series.
The first-order differences are 2,3,5,9,17,332, 3, 5, 9, 17, 33.
Analyzing differences helps determine whether the growth rate follows an arithmetic, geometric, or polynomial rule.
2
Compute the second-order differences of the first-order difference sequence.
The second-order differences are 1,2,4,8,161, 2, 4, 8, 16.
Because the first-order differences do not show an obvious linear pattern, evaluating higher-order differences is necessary.
3
Identify the underlying rule governing the second-order differences.
The second-order sequence doubles with each step (20,21,22,23,24,…2^0, 2^1, 2^2, 2^3, 2^4, \dots). The next second-order difference is 16×2=3216 \times 2 = 32.
Recognizing geometric doubling (2n2^n) allows for projecting the next step accurately.
4
Reconstruct the next first-order difference and calculate the required next sequence value.
Next first-order difference =33+32=65= 33 + 32 = 65. Next series term =72+65=137= 72 + 65 = 137.
Working backward through the difference layers yields the exact value of the next term.

Key Concept

Double-Difference Series with Geometric Progression
Estimated Time:2m 0s
Question 4Question →
Consider the following numerical series:
4,11,30,85,248,…4, 11, 30, 85, 248, \dots
What is the numerical value of the next term in this series?
Show answer & explanation

Answer: 735

Answer

735
Each term is generated by multiplying the preceding term by 3 and subtracting consecutive odd numbers starting from 1 (1,3,5,7,91, 3, 5, 7, 9). Therefore, the term following 248 is computed as (248×3)−9=735(248 \times 3) - 9 = 735.

Step-by-Step Solution

1
Examine the multiplier and subtractor progression between consecutive terms.
Multiplier is constantly 3, while subtractors follow the odd number sequence 1,3,5,7,…1, 3, 5, 7, \dots
Establishing a standard recurrence rule Tn=3⋅Tn−1−(2n−3)T_n = 3 \cdot T_{n-1} - (2n - 3) for n≥2n \ge 2.
2
Calculate the sixth term using the derived rule.
T6=(248×3)−9=744−9=735T_6 = (248 \times 3) - 9 = 744 - 9 = 735
The fifth term is 248, and the fifth odd integer to subtract is 9.

Key Concept

Mixed operation numerical series involving constant multiplication and arithmetic progression of subtractors
Estimated Time:2m 0s
Question 5Question →

In the following number sequence, a specific mathematical pattern is followed:

7,14,25,42,67,?7, 14, 25, 42, 67, ?

What is the value of the missing term represented by the question mark?

Show answer & explanation

Answer: 102

Answer

The missing term in the series is 102.
The correct answer is 102. The sequence is governed by a double difference pattern. The consecutive differences between terms are 7, 11, 17, and 25. The differences of these differences are 4, 6, and 8, which increase by 2 at each step. Thus, the next second difference is 10, the next term difference is 35, and the next term in the sequence is 67 + 35 = 102.

Step-by-Step Solution

1
Find the first-order differences between consecutive terms.
The differences are 7, 11, 17, and 25.
Analyzing first differences helps determine if the growth rate follows a recognizable secondary pattern.
2
Find the second-order differences.
The differences between the consecutive first differences are 4, 6, and 8.
Since the first differences are non-linear, second-order differences reveal the underlying constant acceleration (+2).
3
Project the next first-order difference using the second-order pattern.
The next second-order difference is 10 (since 8 + 2 = 10), making the next first-order difference 25 + 10 = 35.
Extrapolating the arithmetic pattern of the second differences yields the correct next increment.
4
Add the projected difference to the last term of the sequence.
67 + 35 = 102.
Applying the calculated increment to the last term completes the series.

Key Concept

Second-order arithmetic sequence (Double Difference Series)
Question 6Question →

In the given alphanumeric sequence, which term logically comes next to complete the series: A2,D4,G8,J16,…A2, D4, G8, J16, \dots?

Show answer & explanation

Answer: M32M32

Answer

M32M32
The correct answer combines the letter 'M' (obtained by adding 3 forward steps from 'J' in the English alphabet) and the number 32 (obtained by multiplying 16 by 2).

Step-by-Step Solution

1
Analyze the letter progression pattern
The letters follow a pattern of adding 3 positions: A(1)+3=D(4)A (1) + 3 = D (4), D(4)+3=G(7)D (4) + 3 = G (7), G(7)+3=J(10)G (7) + 3 = J (10), and J(10)+3=M(13)J (10) + 3 = M (13).
Identify the rule governing the alphabetical component of the sequence.
2
Analyze the number progression pattern
The numbers follow a pattern of doubling: 2×2=42 \times 2 = 4, 4×2=84 \times 2 = 8, 8×2=168 \times 2 = 16, and 16×2=3216 \times 2 = 32.
Identify the rule governing the numerical component of the sequence.
3
Combine the letter and number terms to find the next element
Combining the 13th letter (MM) and the calculated number (3232) gives M32M32.
Formulate the final term of the series.

Key Concept

Alphanumeric Series Completion
Question 7Question →

Complete the given number series by determining the missing term that logically fits the sequence.

Fill in the blanks below

In the numerical series $6, 13, 27, 48, 76, $, the value of the missing term is .
Show answer & explanation

Answer

The missing term in the series is 111.
The differences between successive terms form an increasing sequence of multiples of 7: +7,+14,+21,+28,…+7, +14, +21, +28, \dots The next difference must be +35+35. Adding 3535 to 7676 yields 111111.

Step-by-Step Solution

1
Calculate the first-order differences between consecutive terms in the series.
13−6=713 - 6 = 7, 27−13=1427 - 13 = 14, 48−27=2148 - 27 = 21, 76−48=2876 - 48 = 28
To identify the underlying pattern governing the progression of the sequence.
2
Analyze the sequence of differences.
The differences are 7,14,21,287, 14, 21, 28, which form an arithmetic progression with a common difference of 77 (multiples of 77).
To determine the next required addition to the sequence.
3
Determine the next difference and compute the missing term.
The next difference is 28+7=3528 + 7 = 35. Adding this to the last term gives 76+35=11176 + 35 = 111.
Applying the identified pattern yields the correct missing term.

Key Concept

Double Difference / Arithmetic Progression of Differences
Estimated Time:1m 0s
Question 8Question →

Determine the underlying double-pattern rule governing the alphanumeric series below and find the term that logically completes it.

Fill in the blanks below

In the sequence Z12,X25,U52,Q107,L218,…Z12, X25, U52, Q107, L218, \dots, the missing term that should replace the blank is .
Show answer & explanation

Answer

The missing term in the sequence is F441.
The sequence consists of two distinct intertwined logic rules: the letter component decreases positional value by progressive increments (-2, -3, -4, -5, -6), turning L (12th letter) into F (6th letter). The numerical component follows the recurrence formula Tn=2×Tn−1+(n−1)T_{n} = 2 \times T_{n-1} + (n-1), where the additive constant increases by 1 each step (+1, +2, +3, +4, +5), yielding 218×2+5=441218 \times 2 + 5 = 441. Combining both gives F441.

Step-by-Step Solution

1
Analyze the alphabetical component by converting letters to their corresponding numerical positions in the alphabet (A=1, B=2, ..., Z=26).
The letter sequence corresponds to positions: Z (26), X (24), U (21), Q (17), L (12).
Tracking positional values helps identify decremental positional shifts.
2
Determine the difference pattern between consecutive letter positions.
26 - 2 = 24 (X); 24 - 3 = 21 (U); 21 - 4 = 17 (Q); 17 - 5 = 12 (L). The positional shift decreases by consecutive integers (-2, -3, -4, -5).
The next shift must be -6, giving position 12 - 6 = 6, which corresponds to the letter F.
3
Analyze the numerical component of the series: 12, 25, 52, 107, 218.
12 × 2 + 1 = 25; 25 × 2 + 2 = 52; 52 × 2 + 3 = 107; 107 × 2 + 4 = 218.
The numerical pattern multiplies the preceding term by 2 and adds an incrementing integer starting from +1.
4
Calculate the next numerical term using the derived recurrence rule.
218 × 2 + 5 = 436 + 5 = 441.
Applying the next multiplier and additive step (×2 + 5) yields 441.
5
Combine the letter and number components.
The completed missing term is F441.
Combining the 6th letter 'F' and calculated number '441' forms the full missing term.

Key Concept

Interleaved positional decrements combined with linear multiplicative-additive recurrence relation.
Estimated Time:2m 0s
Question 9Question →

Determine the missing term that logically completes the given alphanumeric series.

Fill in the blanks below

Consider the following multi-pattern sequence: $$A0, D6, I24, P60, $$ What term should replace the blank to complete the series?
Show answer & explanation

Answer

The term that completes the series is Y120.
The sequence operates on two synchronized rules: the letter in the nn-th position corresponds to the n2n^2-th letter of the alphabet (12=1→A1^2=1 \rightarrow A, 22=4→D2^2=4 \rightarrow D, 32=9→I3^2=9 \rightarrow I, 42=16→P4^2=16 \rightarrow P, 52=25→Y5^2=25 \rightarrow Y), while the numerical portion follows the cubic sequence n3−nn^3 - n (13−1=01^3-1=0, 23−2=62^3-2=6, 33−3=243^3-3=24, 43−4=604^3-4=60, 53−5=1205^3-5=120). Combining both results in Y120.

Step-by-Step Solution

1
Analyze the pattern governing the letter component (A,D,I,P,…A, D, I, P, \dots).
Alphabetical positions are A=1,D=4,I=9,P=16A=1, D=4, I=9, P=16, which follow perfect squares 12,22,32,421^2, 2^2, 3^2, 4^2.
Determining positional index patterns establishes the letter rule for the nn-th term.
2
Determine the letter for the 5th term (n=5n=5).
The position is 52=255^2 = 25, corresponding to the letter YY.
Applying the identified square positional rule yields the 25th alphabet letter.
3
Analyze the pattern governing the numerical component (0,6,24,60,…0, 6, 24, 60, \dots).
The numerical terms follow the polynomial formula n3−nn^3 - n for term indices n=1,2,3,4n = 1, 2, 3, 4.
Evaluating differences (6,18,36…6, 18, 36\dots) reveals a cubic relation n3−nn^3 - n (13−1=0,23−2=6,33−3=24,43−4=601^3-1=0, 2^3-2=6, 3^3-3=24, 4^3-4=60).
4
Calculate the numerical value for n=5n=5.
53−5=125−5=1205^3 - 5 = 125 - 5 = 120.
Substituting n=5n=5 into the cubic polynomial gives the 5th numerical term.
5
Combine the letter and numerical components.
The completed term is Y120.
Joining the 5th letter YY with the 5th numerical value 120120 provides the final answer.

Key Concept

Alphanumeric Series Integration with Perfect Square Letter Indexing and Cubic Polynomial Sequences
Question 10Question →

What is the next letter in the given alphabetical series: Z,X,V,T,R,…Z, X, V, T, R, \dots?

Show answer & explanation

Answer: PP

Answer

The correct next letter in the sequence is PP.
Each term in the series moves backward by 2 steps in the standard English alphabet: Z(26)→X(24)→V(22)→T(20)→R(18)Z (26) \rightarrow X (24) \rightarrow V (22) \rightarrow T (20) \rightarrow R (18). Continuing this constant decrease of 2 leads to the 16th letter, which is PP.

Step-by-Step Solution

1
Determine the alphabetical positions of each given letter in the series
Z=26Z = 26, X=24X = 24, V=22V = 22, T=20T = 20, R=18R = 18
Converting letters to numerical positions helps reveal the mathematical pattern.
2
Identify the common difference between consecutive terms
24−26=−224 - 26 = -2, 22−24=−222 - 24 = -2, 20−22=−220 - 22 = -2, 18−20=−218 - 20 = -2
Each letter is obtained by moving 2 positions backward in the alphabet.
3
Apply the pattern to find the next position and letter
18−2=1618 - 2 = 16, which corresponds to the letter PP
Subtracting 2 positions from the 18th letter (RR) gives the 16th letter (PP).

Key Concept

Reverse Alphabetical Positional Shifts
Question 11Question →
Consider the following multi-pattern alphanumeric sequence:
D4W,G9T,L16P,S35K,D66E,…D4W, G9T, L16P, S35K, D66E, \dots
Which of the following terms logically completes the sequence?
Show answer & explanation

Answer: Q137XQ137X

Answer

The term that logically completes the sequence is Q137XQ137X.
The next term in the sequence is obtained by synthesizing three distinct rules: the first letter moves forward by consecutive prime steps (+13+13 from DD yields QQ), the number multiplies by 22 and adds 55 to yield 137137, and the trailing letter moves +7+7 steps in reverse positional values (EE at reverse index 22 moves to 29, which is reverse index 3 or letter XX). Combining these gives Q137XQ137X.

Step-by-Step Solution

1
Analyze the first letter progression: D→G→L→S→D→?D \rightarrow G \rightarrow L \rightarrow S \rightarrow D \rightarrow ?
Alphabetical positions (1 to 26): D=4,G=7,L=12,S=19,D=30≡4(mod26)D=4, G=7, L=12, S=19, D=30 \equiv 4\pmod{26}. The step differences are +3,+5,+7,+11+3, +5, +7, +11, which are prime numbers. The next prime increment is +13+13. Adding 1313 to D(4)D(4) gives 1717, corresponding to letter QQ.
The first letter advances according to consecutive prime increments modulo 26.
2
Analyze the numerical middle component: 4,9,16,35,66,?4, 9, 16, 35, 66, ?
9=2(4)+19 = 2(4) + 1, 16=2(9)−216 = 2(9) - 2, 35=2(16)+335 = 2(16) + 3, 66=2(35)−466 = 2(35) - 4. Following Nk=2Nk−1+(−1)k+1kN_k = 2 N_{k-1} + (-1)^{k+1} k, the next term is 2(66)+5=1372(66) + 5 = 137.
The numerical pattern multiplies the previous number by 2 and alternates adding/subtracting sequential integers.
3
Analyze the second letter progression using reverse positional values: W,T,P,K,E,?W, T, P, K, E, ?
Reverse positions (Z=1,Y=2,…,A=26Z=1, Y=2, \dots, A=26): W=4,T=7,P=11,K=16,E=22W=4, T=7, P=11, K=16, E=22. Increments in reverse positions are +3,+4,+5,+6+3, +4, +5, +6. The next reverse position increment is +7+7, giving 22+7=29≡3(mod26)22 + 7 = 29 \equiv 3\pmod{26}. Reverse position 3 corresponds to forward letter XX (27−3=2427 - 3 = 24).
The second letter steps through increasing increments in reverse alphabetical indexing.

Key Concept

Multi-pattern alphanumeric series involving prime positional shifts, alternating linear recursive relations, and reverse alphabetical indexing.
Estimated Time:2m 30s
Question 12Question →

Analyze the numerical progression below to determine the rule governing the sequence. What is the value of the missing term that completes the series?

Fill in the blanks below

Consider the series: $$7, 16, 41, 90, 171, $$
Show answer & explanation

Answer

The missing term that completes the sequence is 292.
The difference between successive terms follows the sequence of squares of consecutive odd numbers: 32=93^2 = 9, 52=255^2 = 25, 72=497^2 = 49, 92=819^2 = 81, and 112=12111^2 = 121. Adding 121121 to 171171 gives the missing term 292292.

Step-by-Step Solution

1
Calculate the differences between consecutive terms in the series.
16−7=916 - 7 = 9, 41−16=2541 - 16 = 25, 90−41=4990 - 41 = 49, 171−90=81171 - 90 = 81
Examining first-order differences helps uncover the underlying pattern.
2
Identify the mathematical relationship between the difference values.
The differences are 9,25,49,819, 25, 49, 81, which correspond to 32,52,72,923^2, 5^2, 7^2, 9^2.
The increments between consecutive terms represent the squares of consecutive odd integers starting from 3.
3
Calculate the next term in the sequence using the identified rule.
The next odd number after 99 is 1111, so the required increment is 112=12111^2 = 121. Adding this increment to the last given term gives 171+121=292171 + 121 = 292.
Applying the pattern's next step yields the correct missing term.

Key Concept

Series Completion using Differences of Squares of Consecutive Odd Numbers
Question 13Question →
Which of the following terms logically completes the given alphanumeric series?
C24X,F20U,I16R,L12O,?C24X, \quad F20U, \quad I16R, \quad L12O, \quad ?
Show answer & explanation

Answer: O8LO8L

Answer

O8LO8L
The term containing O8LO8L is correct because it satisfies all three independent series rules: the first letter advances by 3 (L+3=OL + 3 = O), the middle number decreases by 4 (12−4=812 - 4 = 8), and the third letter shifts backward by 3 (O−3=LO - 3 = L).

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term
The first letters follow the sequence: C(3)→+3F(6)→+3I(9)→+3L(12)→+3O(15)C (3) \xrightarrow{+3} F (6) \xrightarrow{+3} I (9) \xrightarrow{+3} L (12) \xrightarrow{+3} O (15).
The first letter advances by 3 positions in alphabetical order.
2
Analyze the pattern of the numerical term
The numbers follow the sequence: 24→−420→−416→−412→−4824 \xrightarrow{-4} 20 \xrightarrow{-4} 16 \xrightarrow{-4} 12 \xrightarrow{-4} 8.
Each number decreases by a constant difference of 4.
3
Analyze the pattern of the last letter in each term
The last letters follow the sequence: X(24)→−3U(21)→−3R(18)→−3O(15)→−3L(12)X (24) \xrightarrow{-3} U (21) \xrightarrow{-3} R (18) \xrightarrow{-3} O (15) \xrightarrow{-3} L (12).
The last letter moves backward by 3 positions in alphabetical order.
4
Combine the resulting components
Combining OO, 88, and LL yields the missing term O8LO8L.
Synthesizing all three independent rules completes the sequence.

Key Concept

Alphanumeric Series Completion with Simultaneous Forward-Reverse Letter Shifts and Arithmetic Decrement
Estimated Time:1m 0s
Question 14Question →

Analyze the pattern in the numerical sequence given below:

4,9,20,43,90,?4, \quad 9, \quad 20, \quad 43, \quad 90, \quad ?

What is the value of the missing term that completes the sequence?

Show answer & explanation

Answer: 185

Answer

185
Each consecutive term is calculated by doubling the previous term and adding an increasing integer (+1,+2,+3,+4,+5+1, +2, +3, +4, +5). Following this rule, 90×2+5=18590 \times 2 + 5 = 185.

Step-by-Step Solution

1
Examine differences or operations between adjacent terms
9−4=59 - 4 = 5, 20−9=1120 - 9 = 11, 43−20=2343 - 20 = 23, 90−43=4790 - 43 = 47
Identify the primary numerical increment pattern
2
Analyze the rule for term progression
The operations follow Tn=Tn−1×2+(n−1)T_n = T_{n-1} \times 2 + (n-1) for n≥2n \ge 2
Confirm consistency across all given terms
3
Compute the sixth term (T6T_6)
T6=90×2+5=185T_6 = 90 \times 2 + 5 = 185
Apply the addition increment +5+5 following +4+4

Key Concept

Number and Alphabet Series
Question 15Question →

Analyze the logical rule governing the given alphanumeric sequence and determine the missing term to complete the series.

Fill in the blanks below

Consider the following series:

$$C5, F12, J27, O51, , B133$$

The term that logically completes the sequence is .
Show answer & explanation

Answer

The missing term that logically completes the series is U86.
The series follows a dual pattern structure. The letter sequence shifts by increasing steps of +3,+4,+5,+6,+7+3, +4, +5, +6, +7, mapping OO (position 15) to UU (position 21). The numerical sequence exhibits a second-order difference pattern (7,15,24,35,477, 15, 24, 35, 47 with underlying difference increase +8,+9,+10,+11+8, +9, +10, +11), adding 3535 to 5151 to yield 8686. Thus, the correct combined term is U86.

Step-by-Step Solution

1
Analyze the pattern of the alphabetical component.
Alphabetical positions follow a sequence of increasing shifts: +3,+4,+5,+6,+7+3, +4, +5, +6, +7.
The alphabetical positions are C=3C = 3, F=6F = 6, J=10J = 10, and O=15O = 15. The differences between consecutive letter positions are 6−3=+36 - 3 = +3, 10−6=+410 - 6 = +4, and 15−10=+515 - 10 = +5. Continuing this progression, the next shift is +6+6, which gives 15+6=2115 + 6 = 21, corresponding to the letter UU. Verification for the subsequent term gives position 21+7=2821 + 7 = 28, which wraps around the 26-letter alphabet to 28−26=228 - 26 = 2, corresponding to BB.
2
Analyze the pattern of the numerical component.
The differences between successive numerical terms form a secondary arithmetic sequence with a common difference of +1+1.
The numerical terms are 5,12,27,515, 12, 27, 51. Taking the first differences between consecutive terms: 12−5=712 - 5 = 7, 27−12=1527 - 12 = 15, and 51−27=2451 - 27 = 24. Taking the second differences: 15−7=815 - 7 = 8 and 24−15=924 - 15 = 9. The second difference increases by +1+1 at each step. Thus, the next first difference must be 24+10=3424 + 10 = 34, making the missing numerical term 51+35=8651 + 35 = 86. Verifying the final term: the next first difference is 35+11=4635 + 11 = 46 (or 35+12=4735 + 12 = 47 when tracking 7,15,24,35,477, 15, 24, 35, 47 with second differences 8,9,10,118, 9, 10, 11), giving 86+47=13386 + 47 = 133.
3
Combine the alphabetical and numerical components.
The complete missing term is U86.
Combining the letter UU with the number 8686 yields the missing term U86U86.

Key Concept

Alphanumeric Series with Positional Shifts and Second-Order Differences
Estimated Time:2m 0s
Question 16Question →
Consider the following alphanumeric series:
A2,D6,G12,J20,…A2, D6, G12, J20, \dots
Which term logically completes the series?
Show answer & explanation

Answer: M30M30

Answer

M30M30
The series consists of two independent rules: the alphabetical components advance by +3+3 positions (A→D→G→J→MA \rightarrow D \rightarrow G \rightarrow J \rightarrow M), and the numerical components follow a pattern of adding successive even numbers (+4,+6,+8,+10+4, +6, +8, +10), leading to 20+10=3020 + 10 = 30. Combining these yields the term M30M30.

Step-by-Step Solution

1
Analyze the pattern in the letter sequence.
A(1)+3=D(4)A (1) + 3 = D (4), D(4)+3=G(7)D (4) + 3 = G (7), G(7)+3=J(10)G (7) + 3 = J (10), J(10)+3=M(13)J (10) + 3 = M (13).
The letters progress forward by 3 positions in the standard alphabetical order.
2
Analyze the pattern in the numeric sequence.
2+4=62 + 4 = 6, 6+6=126 + 6 = 12, 12+8=2012 + 8 = 20, 20+10=3020 + 10 = 30.
The difference between consecutive numbers increases by 22 at each step (+4,+6,+8,+10+4, +6, +8, +10).
3
Combine the next letter and number.
The next term is M30M30.
Combining the 13th letter MM with the calculated number 3030 completes the sequence.

Key Concept

Dual-pattern alphanumeric series progression involving constant letter shifts and increasing even number differences.
Estimated Time:45s
Question 17Question →

Which of the following terms logically completes the given alphanumeric series: C5X,F11U,I19R,L29O,…C5X, F11U, I19R, L29O, \dots?

Show answer & explanation

Answer: O41LO41L

Answer

The term O41LO41L logically completes the given alphanumeric series.
The series follows three simultaneous patterns: the first letter advances by +3+3 positions (C→F→I→L→OC \to F \to I \to L \to O), the middle number increases by successive even integers +6,+8,+10,+12+6, +8, +10, +12 (5→11→19→29→415 \to 11 \to 19 \to 29 \to 41), and the last letter moves backward by −3-3 positions (X→U→R→O→LX \to U \to R \to O \to L). Combining these three components yields O41LO41L.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term.
The sequence of first letters is C(3),F(6),I(9),L(12)C (3), F (6), I (9), L (12).
The alphabetical positions increase by +3+3 each step. Thus, the next letter is at position 12+3=1512 + 3 = 15, which corresponds to OO.
2
Analyze the numerical progression in the middle of each term.
The numerical sequence is 5,11,19,295, 11, 19, 29.
The consecutive differences between terms are 11−5=611 - 5 = 6, 19−11=819 - 11 = 8, and 29−19=1029 - 19 = 10. The difference increases by +2+2 each step. The next difference is 10+2=1210 + 2 = 12, making the next number 29+12=4129 + 12 = 41.
3
Analyze the pattern of the third letter in each term.
The sequence of third letters is X(24),U(21),R(18),O(15)X (24), U (21), R (18), O (15).
The alphabetical positions decrease by −3-3 each step. Thus, the next letter is at position 15−3=1215 - 3 = 12, which corresponds to LL.
4
Combine the elements to find the missing term.
Combining the results yields O41LO41L.
Joining the first letter (OO), middle number (4141), and last letter (LL) completes the sequence.

Key Concept

Tri-pattern Alphanumeric Series Completion
Question 18Question →

In a given alphanumeric sequence, each term consists of a letter and a number following distinct logical patterns:

Z4,U9,Q19,N39,L79,…Z4, U9, Q19, N39, L79, \dots

What is the next term in this sequence?

Show answer & explanation

Answer: K159

Answer

The term that logically completes the sequence is K159.
The correct answer combines the letter obtained from a diminishing positional shift (L minus 1 position equals K) with the number calculated via double-plus-one recursion (79 multiplied by 2 plus 1 equals 159).

Step-by-Step Solution

1
Analyze the alphabetical component shift pattern
Z (26) to U (21) is -5; U (21) to Q (17) is -4; Q (17) to N (14) is -3; N (14) to L (12) is -2.
Identifying the step interval between consecutive position numbers reveals a decreasing shift pattern (-5, -4, -3, -2).
2
Determine the next letter in the series
From L (12), subtract 1: 12 - 1 = 11, which corresponds to the letter K.
Following the decreasing shift pattern (-5, -4, -3, -2, -1), the next letter position is 11.
3
Analyze the numerical component progression
4 to 9: 4 × 2 + 1 = 9; 9 to 19: 9 × 2 + 1 = 19; 19 to 39: 19 × 2 + 1 = 39; 39 to 79: 39 × 2 + 1 = 79.
Each number term is calculated by multiplying the previous term by 2 and adding 1.
4
Compute the next numerical term
79 × 2 + 1 = 158 + 1 = 159.
Applying the recursive formula gives 159 for the sixth term.

Key Concept

Alphanumeric Series Completion with Decrementing Positional Shifts and Double-Plus-One Numerical Recurrence
Question 19Question →
Determine the next term that logically completes the following numerical sequence:
4,7,14,27,48,79,…4, 7, 14, 27, 48, 79, \dots
Show answer & explanation

Answer: 122

Answer

The next term in the sequence is 122.
The sequence follows a double-difference pattern. The differences between successive terms are 3, 7, 13, 21, 31. Taking the differences of these values gives 4, 6, 8, 10, which increases by 2 each time. The next second-order difference must be 12, making the next first-order difference 31 + 12 = 43. Adding 43 to 79 gives the final result of 122.

Step-by-Step Solution

1
Calculate the first-order differences between consecutive terms
The first differences are 3, 7, 13, 21, and 31.
Identifying the rate of increase helps determine the underlying rule.
2
Calculate the second-order differences
The second differences are 4, 6, 8, and 10.
Since the first differences are not constant, analyzing second-level differences reveals higher-order patterns.
3
Extend the second-difference pattern to find the next first difference and term
Next second difference = 12, next first difference = 43, next term = 79 + 43 = 122.
The second differences form an arithmetic sequence adding 2 at each step.

Key Concept

Double-Difference Numerical Series
Question 20Question →
Consider the following numerical sequence:
5,14,19,54,83,…5, 14, 19, 54, 83, \dots
What is the value of the next term in this sequence?
Show answer & explanation

Answer: 202

Answer

The next term in the numerical sequence is 202.
The sequence follows the recurrence pattern an=2an−1+(−1)nn2a_n = 2 a_{n-1} + (-1)^n n^2 starting with a1=5a_1 = 5. To find the 6th term, double the 5th term (83×2=16683 \times 2 = 166) and add 62=366^2 = 36, resulting in 166+36=202166 + 36 = 202.

Step-by-Step Solution

1
Identify the operation connecting the first two terms (55 and 1414).
a2=2×a1+22=2(5)+4=14a_2 = 2 \times a_1 + 2^2 = 2(5) + 4 = 14
Establishes the initial multiplier and square term offset.
2
Determine the rule for the third, fourth, and fifth terms.
a3=2(14)−32=19a_3 = 2(14) - 3^2 = 19, a4=2(19)+42=54a_4 = 2(19) + 4^2 = 54, a5=2(54)−52=83a_5 = 2(54) - 5^2 = 83
Shows an alternating addition and subtraction of consecutive squares n2n^2 after doubling the previous term.
3
Apply the rule for n=6n=6 to calculate the missing term.
a6=2(83)+62=166+36=202a_6 = 2(83) + 6^2 = 166 + 36 = 202
Since the 5th term subtracted 525^2, the 6th term must add 626^2 to twice the 5th term.

Key Concept

Alternating Operational and Square Offsets in Recursive Series
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