Consider the following alphanumeric series: B4, E9, I19, N39, T79, \dots Which of the foll… — State PSC Exam

Consider the following alphanumeric series:

B4, E9, I19, N39, T79, \dots

Which of the following terms logically completes the series?

$A159$ Answer
B
$Z159$
C
$A158$
D
$Z158$

Answer

The term that logically completes the series is

A159

The letter sequence advances by increasing positional shifts (+3, +4, +5, +6, +7), bringing T (20) to 27, which wraps around to A. The number sequence follows

n_{k} = 2n_{k-1} + 1

, transforming 79 into 159. Combining these yields

A159

Step-by-Step Solution

Analyze the pattern governing the letter component of the series.

Positions in the English alphabet: B is 2, E is 5, I is 9, N is 14, T is 20.
Differences between consecutive letter positions:

5 - 2 = +3

9 - 5 = +4

14 - 9 = +5

20 - 14 = +6

Following this progression, the next shift must be

+7

.
Adding 7 to the position of T (20) gives

20 + 7 = 27

. Wrapping around the 26-letter alphabet (

27 - 26 = 1

), the 1st letter is A.

The letter pattern increases the positional shift increment by 1 at each step.

Analyze the pattern governing the numerical component of the series.

The numerical terms are 4, 9, 19, 39, 79.
Evaluating the relation between consecutive terms:

4 \times 2 + 1 = 9

9 \times 2 + 1 = 19

19 \times 2 + 1 = 39

39 \times 2 + 1 = 79

Applying the same rule to 79:

79 \times 2 + 1 = 159

Each number is generated by doubling the preceding number and adding 1.

Combine the letter and numerical results.

The next term in the series is

A159

Joining the identified letter A with the calculated number 159 yields the complete next term.

Key Concept

Alphanumeric Series Completion via Increasing Positional Shift and Recurrence Progression

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