In the following question, a series is given with one term missing, choose the…
2023
In the following question, a series is given with one term missing, choose the correct alternative from the given options: 1, 2, 6, 15, ____, 56, 92.
Answer: D. 31 — Concept: in a difference-based number series the rule lives in the gaps, not in the terms. Subtract each term from the one that follows it; when those first…
- A.
30
- B.
32
- C.
34
- D.
31
Attempted by 15 students.
Show answer & explanation
Correct answer: D
Concept: in a difference-based number series the rule lives in the gaps, not in the terms. Subtract each term from the one that follows it; when those first differences themselves form a familiar pattern — consecutive natural numbers, consecutive perfect squares, a fixed ratio — that pattern is the rule of the series. Any missing term is then recovered as: previous term + the difference the pattern demands at that position.
Application to this series:
Write the terms in order, marking the unknown fifth term: 1, 2, 6, 15, ?, 56, 92.
Take the differences of the neighbouring known terms: 2 − 1 = 1, 6 − 2 = 4, 15 − 6 = 9.
Read those differences as squares: 1 = 12, 4 = 22, 9 = 32 — the differences run through the consecutive perfect squares.
The gap that carries the 4th term to the 5th is therefore the next square, 42 = 16, so the missing term is 15 + 16 = 31.
Step | Difference | Square form |
|---|---|---|
1 → 2 | 1 | 12 |
2 → 6 | 4 | 22 |
6 → 15 | 9 | 32 |
15 → the blank | 16 | 42 |
the blank → 56 | 25 | 52 |
56 → 92 | 36 | 62 |
Cross-check by running the same rule past the blank: 31 + 52 = 31 + 25 = 56, and 56 + 62 = 56 + 36 = 92. Both printed tail terms are reproduced, so the square-difference rule fits the entire series and not merely its left half.
Missing term = 31.