Compound multipliers – next value with rising percentage factors: 50, 60, 75, 97.5, ?, 184.275, 267.19875

Introduction / Context:
Each term is obtained by multiplying by an increasing percentage factor: ×1.20, ×1.25, ×1.30, ×1.35, ×1.40, ×1.45.

Observation / Approach:

• 50 × 1.20 = 60
• 60 × 1.25 = 75
• 75 × 1.30 = 97.5
• Next factor = 1.35 ⇒ 97.5 × 1.35 = 131.625
• Then ×1.40 ⇒ 131.625 × 1.40 = 184.275
• Then ×1.45 ⇒ 184.275 × 1.45 = 267.19875

Step-by-Step Solution:
Compute 97.5 × 1.35 = 131.625.

Verification / Alternative check:
Forward multiplications match the later given terms exactly, confirming the factor ladder.

Why Other Options Are Wrong:
Other numbers do not equal 97.5 × 1.35 and would not propagate correctly to 184.275 and 267.19875.

Common Pitfalls:
Assuming a constant percentage; the key is the steady +0.05 increase in the multiplier each step.

Final Answer:
131.625