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: 2^2 = 4, 4^2 = 16, 6^2 = 36, 8^2 = 64.

• Even-position terms are squares of consecutive even numbers decreasing by 2: 14^2 = 196, 12^2 = 144, 10^2 = 100, 8^2 = 64.

• Therefore the 8th term, X, is 8^2 = 64, so option (b) follows.

Why the other options are wrong

(a) 48: 48 is not 8^2 and does not continue the even-position pattern 196, 144, 100, X.
(c) 125: 125 is not 8^2 and does not continue the even-position pattern 196, 144, 100, X.
(d) 256: 256 is 16^2, not 8^2, 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.