Question

In the following series find correct options at the place of question mark. 2, 4, 12, 6, 12, 36, 18, 36, 108, ?

• A. 72
• B. 54
• C. 90
• D. 108
• E. 75

Hint:

Look for repeating patterns in groups. Multiply by consistent factors within each group.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is an alternating operation series where a set of rules repeats every few terms.
Step 2: Key Formula or Approach:
Track the operation between consecutive terms: (\(\times 2, \times 3, \div 2\)).
Step 3: Detailed Explanation:
- Term 1 to 2: \( 2 \times 2 = 4 \)
- Term 2 to 3: \( 4 \times 3 = 12 \)
- Term 3 to 4: \( 12 \div 2 = 6 \)
- Term 4 to 5: \( 6 \times 2 = 12 \)
- Term 5 to 6: \( 12 \times 3 = 36 \)
- Term 6 to 7: \( 36 \div 2 = 18 \)
- Term 7 to 8: \( 18 \times 2 = 36 \)
- Term 8 to 9: \( 36 \times 3 = 108 \)
- Term 9 to 10: \( 108 \div 2 = 54 \).
Step 4: Final Answer:
The correct option is 54.