Identify the numbers that occur in the series 1, 7, 17, 31, 49, ...........…
2024
Identify the numbers that occur in the series 1, 7, 17, 31, 49, ...........
(A) 74 (B) 95 (C) 97 (D) 127 (E) 161
Choose the correct answer from the options given below :
- A.
(A), (B), (C) only
- B.
(C), (D), (E) only
- C.
(E), (B), (A) only
- D.
(C), (D), (B) only
Attempted by 10 students.
Show answer & explanation
Correct answer: B
The series is 1, 7, 17, 31, 49. The differences are 6, 10, 14, 18. Since the second difference is constant (4), the general term is quadratic: 2n^2 - 1. Checking the options: (C) 97 gives 2n^2=98 so n=7. (D) 127 gives 2n^2=128 so n=8. (E) 161 gives 2n^2=162 so n=9. Options (A) and (B) do not result in integer n. Therefore, 97, 127, and 161 are in the series.