Consider the following alphanumeric sequence: W7, T14, P26, K45, E73, \dots Which of the f… — State PSC Exam

Consider the following alphanumeric sequence:

W7, T14, P26, K45, E73, \dots

Which of the following options logically completes the sequence?

$X112$ Cevap
B
$Y112$
C
$X110$
D
$Y108$

Cevap

The correct option is

X112

, obtained by shifting the letter term backwards by 7 positions (E to X) and adding 39 to the previous numerical term (73 + 39 = 112) based on the double-difference pattern.

The correct answer is

X112

. The letter pattern subtracts increasing integer steps (-3, -4, -5, -6, -7), where E (5) minus 7 wraps to X (24). The numerical pattern relies on a double difference of consecutive odd numbers (+5, +7, +9, +11), adding 39 to 73 to yield 112.

Adım Adım Çözüm

Analyze the letter progression pattern.

Alphabetical positions: W(23), T(20), P(16), K(11), E(5). The differences are -3, -4, -5, -6. The next shift must be -7.

The step size subtracted from the letter positions increases by 1 at each step.

Calculate the next letter term.

Subtracting 7 steps backwards from E (5):

5 - 7 = -2 \equiv 24 \pmod{26}

, which corresponds to the 24th letter, X.

Cyclic alphabetical wrapping applies when counting backwards past A.

Analyze the numerical progression using first and second differences.

First differences:

14 - 7 = 7

26 - 14 = 12

45 - 26 = 19

73 - 45 = 28

. Second differences:

12 - 7 = 5

19 - 12 = 7

28 - 19 = 9

The second differences form a sequence of consecutive odd numbers (+5, +7, +9).

Compute the next numerical term.

The next second difference is

+11

. Thus, the next first difference is

28 + 11 = 39

. Adding this to the last term yields

73 + 39 = 112

Extrapolating the double-difference pattern determines the missing number.

Anahtar Kavram

Alphanumeric series completion with variable reverse positional letter shifts and double-difference numerical patterns

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