csatmedium

What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X ?

  1. A.48
  2. B.64
  3. C.125
  4. D.256
▶ Answer & Explanation

Correct answer: B. 64

The sequence alternates between two independent patterns. The numbers at odd positions (1st, 3rd, 5th, 7th) are squares of consecutive even numbers: $2^2=4$, $4^2=16$, $6^2=36$, $8^2=64$. The numbers at even positions (2nd, 4th, 6th) are squares of decreasing even numbers: $14^2=196$, $12^2=144$, $10^2=100$. Following this pattern, the next number at an even position would be $8^2$, which is 64. Therefore, X is 64.

Source: UPSC csat 2019

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