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Question

Difficulty: Very hardNumber and Alphabet Series
Consider the following multi-pattern alphanumeric series:
B3Y,E5W,I13T,N49P,T241K,…B3Y, E5W, I13T, N49P, T241K, \dots
Which of the following alphanumeric terms correctly completes the given sequence?
  1. A1441EAnswer
  2. B
    Z1446F
  3. C
    A1440Q
  4. D
    B1441E

Answer

A1441E
The correct term is determined by combining three distinct concurrent rules: the first letter shifts forward by incrementally larger intervals (+3, +4, +5, +6, +7) wrapping from T to A; the middle number follows the operational recurrence relation (Previous × n) - (n - 1) yielding (241 × 6) - 5 = 1441; and the third letter shifts backward by expanding steps (-2, -3, -4, -5, -6) moving from K to E.

Step-by-Step Solution

1
Analyze the pattern of the first letters in the terms: B, E, I, N, T
Positions in alphabet: B(2) → (+3) → E(5) → (+4) → I(9) → (+5) → N(14) → (+6) → T(20). The next shift must be +7. T(20) + 7 = 27, which wraps around to A(1).
The forward positional shift increases by +1 at each successive step.
2
Analyze the pattern of the middle numerical sequence: 3, 5, 13, 49, 241
Step 1 to 2 (n=2): (3 × 2) - 1 = 5. Step 2 to 3 (n=3): (5 × 3) - 2 = 13. Step 3 to 4 (n=4): (13 × 4) - 3 = 49. Step 4 to 5 (n=5): (49 × 5) - 4 = 241. Step 5 to 6 (n=6): (241 × 6) - 5 = 1446 - 5 = 1441.
The operational formula for the nth transition is Term_n = (Term_{n-1} × n) - (n - 1).
3
Analyze the pattern of the third letters in the terms: Y, W, T, P, K
Positions in alphabet: Y(25) → (-2) → W(23) → (-3) → T(20) → (-4) → P(16) → (-5) → K(11). The next shift must be -6. K(11) - 6 = 5, which corresponds to E.
The backward positional shift magnitude increases by 1 step sequentially.
4
Combine the results of the three independent sub-patterns
First letter: A, Middle number: 1441, Last letter: E. Combined term: A1441E.
Formulating the final composite term completing the series.

Key Concept

Multi-layered Alphanumeric Series Completion
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Topics

Number and Alphabet Series

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