Consider the following multi-pattern alphanumeric sequence: D4W, G9T, L16P, S35K, D66E, \d… — State PSC Exam

Consider the following multi-pattern alphanumeric sequence:

D4W, G9T, L16P, S35K, D66E, \dots

Which of the following terms logically completes the sequence?

The term that logically completes the sequence is

Q137X

The next term in the sequence is obtained by synthesizing three distinct rules: the first letter moves forward by consecutive prime steps (

+13

from

D

yields

Q

), the number multiplies by

2

and adds

5

to yield

137

, and the trailing letter moves

+7

steps in reverse positional values (

E

at reverse index 22 moves to 29, which is reverse index 3 or letter

X

). Combining these gives

Q137X

Analyze the first letter progression:

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 \equiv 4\pmod{26}

. The step differences are

+3, +5, +7, +11

, which are prime numbers. The next prime increment is

+13

. Adding

13

D(4)

gives

17

, corresponding to letter

Q

The first letter advances according to consecutive prime increments modulo 26.

Analyze the numerical middle component:

4, 9, 16, 35, 66, ?

9 = 2(4) + 1

16 = 2(9) - 2

35 = 2(16) + 3

66 = 2(35) - 4

. Following

N_k = 2 N_{k-1} + (-1)^{k+1} k

, the next term is

2(66) + 5 = 137

The numerical pattern multiplies the previous number by 2 and alternates adding/subtracting sequential integers.

Analyze the second letter progression using reverse positional values:

W, T, P, K, E, ?

Reverse positions (

Z=1, Y=2, \dots, A=26

W=4, T=7, P=11, K=16, E=22

. Increments in reverse positions are

+3, +4, +5, +6

. The next reverse position increment is

+7

, giving

22 + 7 = 29 \equiv 3\pmod{26}

. Reverse position 3 corresponds to forward letter

X

(

27 - 3 = 24

The second letter steps through increasing increments in reverse alphabetical indexing.

Multi-pattern alphanumeric series involving prime positional shifts, alternating linear recursive relations, and reverse alphabetical indexing.

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