Correct Option (2)

The given sequence is 24, X, 12, 18, 36, 90. To determine the value of X, the underlying pattern of the sequence must be identified.

Upon examining the known terms, a multiplicative pattern can be observed:

From 12 to 18, the multiplier is 18 / 12 = 1.5
From 18 to 36, the multiplier is 36 / 18 = 2.0
From 36 to 90, the multiplier is 90 / 36 = 2.5

This reveals an arithmetic progression in the multipliers, where each successive multiplier increases by 0.5 (i.e., ..., 1.5, 2.0, 2.5). Extending this pattern backward:

The multiplier for the term preceding 12 (i.e., X to 12) must be 1.0 (since 1.5 - 0.5 = 1.0).
The multiplier for the term preceding X (i.e., 24 to X) must be 0.5 (since 1.0 - 0.5 = 0.5).

Applying these derived multipliers:

To find X: 24 * 0.5 = 12. Therefore, X = 12.
To verify: If X = 12, then 12 * 1.0 = 12, which correctly yields the subsequent term in the sequence.

Thus, the value of X is 12.

Incorrect Options:

Options 1 (18), 3 (9), and 4 (6) are incorrect because substituting these values for X does not maintain the established multiplicative pattern where each term is multiplied by a factor increasing by 0.5. For instance, if X were 18, the multipliers would be 24 to 18 (0.75) and 18 to 12 (approximately 0.67), which deviates from the consistent increase of 0.5 observed in the latter part of the sequence.