A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 8, 24, 12, ?, 18, 54

Introduction / Context:
This series alternates between multiplication and division by fixed numbers. Recognising such alternating operation patterns is important in number series questions. The sequence is 8, 24, 12, ?, 18, 54, and we must determine the missing fourth term so that the alternating pattern remains consistent.

Given Data / Assumptions:
- Series: 8, 24, 12, ?, 18, 54.- Exactly one intermediate term is missing.- Values rise, then fall, then rise again, suggesting alternating multiplication and division.- The operations likely use simple integers such as 3 and 2.

Concept / Approach:
We analyse how each term is derived from the previous one. Many exam series use a repeating two-step pattern like multiply by 3, then divide by 2, and so on. If that fits the known terms, we can apply the same rule to identify the missing value.

Step-by-Step Solution:
- From 8 to 24: 24 = 8 * 3 (multiplied by 3).- From 24 to 12: 12 = 24 / 2 (divided by 2).- This suggests a two step cycle: multiply by 3, then divide by 2.- Apply this rule to find the missing term after 12.- From 12 to the next term: 12 * 3 = 36.- From this term to 18: 18 = 36 / 2, which perfectly fits the divide by 2 step.- Finally, 18 to 54 also follows multiply by 3: 18 * 3 = 54.- Therefore, the missing number must be 36.

Verification / Alternative check:
- Reconstruct the series with the pattern: • 8 * 3 = 24. • 24 / 2 = 12. • 12 * 3 = 36. • 36 / 2 = 18. • 18 * 3 = 54.- The operations times 3, divide by 2 repeat throughout, confirming that 36 is correct.

Why Other Options Are Wrong:
- 48, 29, 21 and 24 do not support the consistent multiply by 3 then divide by 2 cycle when inserted between 12 and 18.- For example, if 24 were chosen, the step 24 to 18 would not be a division by 2, and 18 to 54 would not continue the established pattern correctly.

Common Pitfalls:
- Focusing only on the main numbers without listing operations can hide the alternating pattern.- Assuming a single operation such as a fixed difference or ratio does not work here and can mislead candidates.- Miscomputing a division or multiplication step, especially in the middle of the sequence, can obscure the regularity of the pattern.

Final Answer:
The series alternates between multiplying by 3 and dividing by 2, so the missing term is 36.