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

Correct Option (B)

The given sequence is 4, 196, 16, 144, 36, 100, 64, X. This sequence can be analyzed as two alternating sub-series:

• Sub-series 1 (Terms at odd positions: 1st, 3rd, 5th, 7th): 4, 16, 36, 64.
  • These terms are the squares of consecutive even numbers:
  • 4 = 2²
  • 16 = 4²
  • 36 = 6²
  • 64 = 8²
• Sub-series 2 (Terms at even positions: 2nd, 4th, 6th, 8th): 196, 144, 100, X.
  • These terms are the squares of decreasing even numbers:
  • 196 = 14²
  • 144 = 12²
  • 100 = 10²
  • Following this established pattern, the next term in Sub-series 2 would be the square of 8.
  • Therefore, X = 8² = 64.

Incorrect Options:

Options A (48), C (125), and D (256) are incorrect as they do not adhere to the identified numerical patterns of either sub-series within the given sequence. 48 is not a perfect square fitting the pattern. 125 is 5³, not a square in the sequence. 256 is 16², which does not follow the decreasing even number square progression (14², 12², 10², 8²) required for the position of X.