Find the missing term in the geometric-like progression: 4, 12, 36, __, 324, 972.

Introduction / Context:This number pattern multiplies each term by a constant factor to obtain the next term. Recognizing the factor allows us to insert the missing value correctly.

Given Data / Assumptions:

• Sequence: 4, 12, 36, __, 324, 972.
• Terms appear to grow by a constant ratio.

Concept / Approach:

• Check ratio: 12/4 = 3, 36/12 = 3.
• Assume constant ratio 3 continues.

Step-by-Step Solution:

Verification / Alternative check:All ratios equal 3; sequence is consistent after inserting 108.

Why Other Options Are Wrong:

• 125, 215, 312: Do not maintain a constant ratio of 3 throughout.
• None of these: Not applicable; 108 fits perfectly.

Common Pitfalls:

• Trying to apply addition instead of multiplication in geometric-like sequences.

Final Answer:108