Consider the following complex alphanumeric sequence: C3F, E8I, H18L, L38O, Q78R, \dots Wh… — State PSC Exam

Consider the following complex alphanumeric sequence:

C3F, E8I, H18L, L38O, Q78R, \dots

Which of the following terms logically completes the series?

$W158U$ Answer
B
$V158U$
C
$W156U$
D
$W158V$

Answer

W158U

The term is obtained by breaking the alphanumeric code into three parallel streams: (1) First letter follows increasing step intervals (+2, +3, +4, +5, +6), bringing Q (17) to W (23). (2) Numerical component uses the rule

2x + 2

, converting 78 to 158. (3) Second letter has a constant increment of +3, moving R (18) to U (21). Combining these gives the complete term

W158U

Step-by-Step Solution

Analyze the pattern of the first letter in each term

Positions in alphabet: C (3), E (5), H (8), L (12), Q (17). The positional increments are +2, +3, +4, +5. Following this pattern, the next increment must be +6. Adding 6 to Q (17) yields 23, which corresponds to the letter W.

The first element follows an increasing arithmetic step pattern.

Analyze the numerical progression in the terms

Sequence of numbers: 3, 8, 18, 38, 78. The recurrence relation is

N_k = 2 \times N_{k-1} + 2

. Calculating the next value:

2 \times 78 + 2 = 156 + 2 = 158

Each number is formed by doubling the previous term and adding 2.

Analyze the pattern of the second letter in each term

Positions in alphabet: F (6), I (9), L (12), O (15), R (18). The positional increment is constant at +3. Adding 3 to R (18) yields 21, which corresponds to the letter U.

The third element follows a constant positional step pattern.

Synthesize the components to form the final term

Combining the calculated first letter (W), numerical middle value (158), and second letter (U) yields

W158U

All three independent term rules must be combined.

Key Concept

Multi-Pattern Alphanumeric Series Completion

Estimated Time:2m 0s

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