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Difficulty: HardNumber and Alphabet Series

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?

  1. K159Answer
  2. B
    J159
  3. C
    K157
  4. D
    L159

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
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Topics

Number and Alphabet Series

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