Find the missing number in the series: 5, 17, 37, 65, _____, 145
2023
Find the missing number in the series: 5, 17, 37, 65, _____, 145
Answer: A. 101 — ConceptIn a number series, first differences measure the change from one term to the next. When those differences form an arithmetic progression, the constant…
- A.
101
- B.
95
- C.
99
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: A
Concept
In a number series, first differences measure the change from one term to the next.
When those differences form an arithmetic progression, the constant second difference determines each following gap.
Application
Compute the known gaps: 17 − 5 = 12, 37 − 17 = 20, and 65 − 37 = 28.
The gaps rise by 8 each time: 20 − 12 = 8 and 28 − 20 = 8.
Continue the gap pattern: the next gap is 28 + 8 = 36, so the missing term is 65 + 36 = 101.
The following gap is 36 + 8 = 44, giving 101 + 44 = 145.
Cross-check
The complete first-difference sequence is 12, 20, 28, 36, 44; every adjacent pair differs by 8, and the last term returns exactly 145.
Therefore, the missing number is 101.