What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X ?
- (a) 48
- (b) 64 ✓ UPSC's answer
- (c) 125
- (d) 256
Why the answer is (b)
• Split the sequence into two alternating subsequences: odd positions 4, 16, 36, 64 and even positions 196, 144, 100, X.
• Odd-position terms are squares of consecutive even numbers: 2² = 4, 4² = 16, 6² = 36, 8² = 64.
• Even-position terms are squares of consecutive even numbers decreasing by 2: 14² = 196, 12² = 144, 10² = 100, 8² = 64.
• Therefore the 8th term, X, is 8² = 64, so option (b) follows.
Why the other options are wrong
- (a) 48
- 48 is not 8² and does not continue the even-position pattern 196, 144, 100, X.
- (c) 125
- 125 is not 8² and does not continue the even-position pattern 196, 144, 100, X.
- (d) 256
- 256 is 16², not 8², so it does not continue the even-position pattern 196, 144, 100, X.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.