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

• The sequence follows a pattern of alternating multiplication by 0.5 and 1.5, or equivalently, multiplying by 3/2 and 1/2 alternately.

• Starting from the third term (12), the next term is 18, which is 12 × 1.5.

• The term after 18 is 36, which is 18 × 2. Wait, let's re-evaluate the pattern from the end or middle.

• Let's look at the ratios: 12 to 18 is ×1.5; 18 to 36 is ×2; 36 to 90 is ×2.5. This suggests an increasing multiplier pattern: ×1.5, ×2, ×2.5.

• If the pattern of multipliers is increasing by 0.5 each step (×1.5, ×2, ×2.5), then the step before ×1.5 (from X to 12) should be ×1.0? No, that doesn't fit the start.

• Let's try another common pattern: Multiplication by 1.5, then 2, then 2.5, then 3? No.

• Let's look at the differences or a different multiplicative logic.

• Consider the pattern: ×1.5, ×2, ×2.5, ×3.

• If 36 × 2.5 = 90, then 18 × 2 = 36, then 12 × 1.5 = 18.

• Following this backward, the step before 12 (i.e., X to 12) should follow the previous multiplier in the sequence. The multipliers are 1.5, 2, 2.5. The previous one would be 1.0? If X × 1.0 = 12, X=12. But 24 to 12 is ×0.5.

• Let's re-examine: 24, X, 12, 18, 36, 90.

• Ratios: 12/18 = 2/3? No. 18/12 = 1.5. 36/18 = 2. 90/36 = 2.5.

• The multipliers are 1.5, 2, 2.5. The difference is 0.5.

• So the multiplier before 1.5 should be 1.0. Thus, X × 1.0 = 12? No, the sequence is X -> 12. So 12 / X = 1.0? Then X=12.

• Let's check the first step: 24 -> X. If the multiplier pattern is 0.5, 1.0, 1.5, 2.0, 2.5?

• 24 × 0.5 = 12 (This would make X=12, but the next term is 12, so X would be 12? No, the sequence is 24, X, 12. If 24×0.5=12, then X is missing or the pattern is different).

• Let's try: 24 × 0.5 = 12. But the term is X.

• Let's look at the options. If X=12, sequence is 24, 12, 12, 18, 36, 90. Ratios: 0.5, 1, 1.5, 2, 2.5. This is a perfect arithmetic progression of multipliers: 0.5, 1.0, 1.5, 2.0, 2.5.

• Therefore, 24 × 0.5 = 12 (X), 12 × 1.0 = 12, 12 × 1.5 = 18, 18 × 2.0 = 36, 36 × 2.5 = 90.

• The pattern holds perfectly with multipliers increasing by 0.5 each step.