What is X in the sequence 24, X, 12, 18, 36, 90? (a) 18 (b) 12 (c) 9 (d) 6.

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We have a sequence with six terms: twenty-four, X, twelve, eighteen, thirty-six, and ninety. We need to find the value of X from the given options: eighteen, twelve, nine, or six. Let's find the pattern by examining the known terms. Starting from position three, we calculate the ratios between consecutive terms. Eighteen divided by twelve equals one point five. Thirty-six divided by eighteen equals two point zero. Ninety divided by thirty-six equals two point five. The ratios form a pattern: one point five, two point zero, two point five, increasing by zero point five each time. Now we work backwards to find X. If the pattern continues, the ratios before one point five and two point zero should be one point zero and zero point five. From X to twelve, the ratio should be one point zero, so twelve equals X times one point zero, which means X equals twelve. We can verify this: twenty-four times zero point five equals twelve, confirming our answer. The complete sequence is twenty-four, twelve, twelve, eighteen, thirty-six, ninety. The multipliers are zero point five, one point zero, one point five, two point zero, two point five, forming an arithmetic progression with common difference zero point five. Therefore, X equals twelve, which corresponds to option B. To summarize what we learned: We identified a pattern in the ratios between consecutive terms, discovered they form an arithmetic progression, applied this pattern backwards to find the missing term, and verified that X equals twelve, which matches option B.