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

The correct option is 64.

To find the value of $X$ in the sequence, let us analyze the pattern of the given numbers:
4, 196, 16, 144, 36, 100, 64, X

This sequence is an alternating sequence, which consists of two interleaved sub-sequences: one at the odd positions (1st, 3rd, 5th, 7th terms) and one at the even positions (2nd, 4th, 6th, 8th terms).

Let us look at the first sub-sequence (odd-positioned terms):
1st term: 4
3rd term: 16
5th term: 36
7th term: 64

We can write these numbers as squares of consecutive even integers:
$2^2=4$
$4^2=16$
$6^2=36$
$8^2=64$

Now, let us look at the second sub-sequence (even-positioned terms), which contains our unknown value $X$ at the 8th position:
2nd term: 196
4th term: 144
6th term: 100
8th term: X

These terms can also be expressed as squares of even integers, but in descending order starting from 14:
${14}^2=196$
${12}^2=144$
${10}^2=100$

Following this decreasing pattern of even numbers (14, 12, 10, ...), the next base integer for the 8th term must be 8.
Therefore, the value of $X$ is the square of 8:

$X=8^2=64$