What will come in place of * in the sequence 3, 14, 39, 84, *, 258?
- (a) 150
- (b) 155 ✓ UPSC's answer
- (c) 160
- (d) 176
Why the answer is (b)
• Calculate the first differences between consecutive terms: 14 - 3 = 11, 39 - 14 = 25, 84 - 39 = 45.
• Calculate the second differences between the first differences: 25 - 11 = 14, 45 - 25 = 20.
• Calculate the third differences between the second differences: 20 - 14 = 6.
• Assuming the third difference is constant at 6, the next second difference is 20 + 6 = 26.
• The next first difference is 45 + 26 = 71.
• The missing term is 84 + 71 = 155, which matches option (b).
Why the other options are wrong
- (a) 150
- 150 results from an incorrect calculation of the next first difference as 66 instead of 71.
- (c) 160
- 160 results from an incorrect calculation of the next first difference as 76 instead of 71.
- (d) 176
- 176 results from an incorrect calculation of the next first difference as 92 instead of 71.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.