Wrong Term in the Alternating ×2.5 and ×2 Series (with one error): 3, 7.5, 15, 37.5, 75, 167.5, 375 — identify the lone incorrect term.

Introduction / Context:Alternating-multiplier series frequently toggle between two simple factors. Here, the intended pattern is ×2.5, then ×2, repeating.

Given Data / Assumptions:

• Given series: 3, 7.5, 15, 37.5, 75, 167.5, 375.
• Intended pattern: multiply alternately by 2.5 and 2.

Concept / Approach:Apply the alternating multipliers and compare expected vs given terms to find the mismatch.

Step-by-Step Solution:3 × 2.5 = 7.5 ✓7.5 × 2 = 15 ✓15 × 2.5 = 37.5 ✓37.5 × 2 = 75 ✓75 × 2.5 = 187.5 (but given 167.5) ✗Continuing the intended rule: 187.5 × 2 = 375 ✓

Verification / Alternative check:All positions agree with the alternating ×2.5 and ×2 pattern except the 6th term, which must be 187.5, not 167.5.

Why Other Options Are Wrong:

• 37.5, 75, 15, 375: each aligns with the intended alternating multipliers.

Common Pitfalls:Rounding or copying errors at the 6th term. The multipliers are exact; no rounding is needed.

Final Answer:167.5