Number Series — Constant Ratio (Geometric Progression) Find the next number in the sequence: 4, 12, 36, 108, ?

Introduction / Context:Here the growth is multiplicative with a constant ratio, a hallmark of a geometric progression. Identifying the multiplier gives the next term immediately.

Given Data / Assumptions:

• Series: 4, 12, 36, 108, ?
• Check the ratio between consecutive terms.

Concept / Approach:In a geometric progression, each term equals the previous term multiplied by a constant r. Determine r and apply once more to find the missing term.

Step-by-Step Solution:12 / 4 = 336 / 12 = 3108 / 36 = 3Common ratio r = 3Next term = 108 * 3 = 324

Verification / Alternative check:The ratio remains constant at 3 across all visible steps. Extending once yields 324, consistent with the pattern.

Why Other Options Are Wrong:

• 144, 216, 304: These are not equal to 108 * 3 and thus break the geometric rule.

Common Pitfalls:Mistaking additive patterns for multiplicative ones. Always check both differences and ratios in fast sequence analysis.

Final Answer:324