What is X in the sequence 24, X, 12, 18, 36, 90?

The correct option is 12.

To find the missing term $X$ in the sequence 24, $X$, 12, 18, 36, 90, let us analyze the relationship between consecutive numbers in the series.

Let us examine the ratio of each term to the preceding term starting from the known values later in the sequence:

To get 18 from 12:
$12\times 1.5=18$

To get 36 from 18:
$18\times 2=36$

To get 90 from 36:
$36\times 2.5=90$

We can see a clear pattern where each successive term is obtained by multiplying the previous term by a multiplier that increases by 0.5 at each step:

Multiplier sequence: 0.5, 1.0, 1.5, 2.0, 2.5, ...

Applying this pattern from the beginning of the sequence:

First step ($24\to X$):
$X=24\times 0.5=12$

Second step ($X\to 12$):
$12\times 1.0=12$

This confirms that $X=12$ satisfies the entire sequence pattern perfectly.