What number would replace the question mark (?) in the series given below? 1,…
2024
What number would replace the question mark (?) in the series given below? 1, 7, 16, 28, 43, 61, 82, ?
Answer: C. 106 — Concept: In a difference sequence, subtract consecutive terms and inspect how the differences change. If the first differences form an arithmetic progression,…
- A.
102
- B.
143
- C.
106
- D.
110
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept: In a difference sequence, subtract consecutive terms and inspect how the differences change.
If the first differences form an arithmetic progression, extend that progression before adding the next difference to the last term.
Application
Compute the consecutive differences: 7 − 1 = 6, 16 − 7 = 9, 28 − 16 = 12, 43 − 28 = 15, 61 − 43 = 18, and 82 − 61 = 21.
The differences 6, 9, 12, 15, 18, 21 increase by 3 each time, so the next difference is 21 + 3 = 24.
Add this next difference to the last term: 82 + 24 = 106.
Cross-check
The second differences are all 3, and 24 − 21 = 3 preserves that pattern.
Result: Therefore, the missing number is 106.