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Difficulty: HardNumber and Alphabet Series

Consider the following alphanumeric sequence:

B2D,E6H,J14N,Q30V,…B2D, E6H, J14N, Q30V, \dots

Which of the following terms correctly completes the given series?

  1. Z62FAnswer
  2. B
    Y62F
  3. C
    Z62E
  4. D
    A60F

Answer

The term that correctly completes the given alphanumeric series is Z62F.
The correct term is obtained by breaking down the alphanumeric pattern into three separate sub-series. The first letter advances by odd increments (+3, +5, +7, +9) from B to Z. The middle number doubles and adds 2 at each step (2×30+2=622 \times 30 + 2 = 62). The third letter advances by even increments (+4, +6, +8, +10) from D to F (with alphabet wrap-around). Combining these yields Z62F.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term.
The alphabetical positions of the first letters are B (2), E (5), J (10), Q (17). The differences between consecutive terms are +3+3, +5+5, and +7+7. The next difference must be +9+9. Adding +9+9 to Q (17) yields 17+9=2617 + 9 = 26, which corresponds to the letter Z.
The first letter follows an increasing sequence of consecutive odd integer positional shifts.
2
Analyze the numerical pattern in the middle of each term.
The numbers are 2, 6, 14, 30. The progression rule is nk+1=2×nk+2n_{k+1} = 2 \times n_k + 2. Applying this to the last known number: 2×30+2=622 \times 30 + 2 = 62.
Each number is generated by doubling the previous number and adding 2.
3
Analyze the pattern of the third letter in each term.
The alphabetical positions of the third letters are D (4), H (8), N (14), V (22). The positional shifts are +4+4, +6+6, +8+8. The next shift must be +10+10. Adding +10+10 to V (22) gives 22+10=3222 + 10 = 32. Modulo 26 alphabet cycle gives 32−26=632 - 26 = 6, which corresponds to the letter F.
The third letter follows an increasing sequence of consecutive even integer positional shifts with alphabetical wrap-around.
4
Combine the derived components into the final term.
Combining the first letter (Z), the number (62), and the third letter (F) gives Z62F.
The complete term must satisfy all three sub-patterns simultaneously.

Key Concept

Alphanumeric Series Completion with Multi-Pattern Positional Shifts and Arithmetic Operations
Estimated Time:2m 0s
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Topics

Number and Alphabet Series

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