JAMB 2020 Mathematics · Question 6
Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio
Options
- A.
- B.
- C.
- D.
Answer: A.
Explanation written with AI and checked against the answer key
Analyze the question: In a geometric progression (GP), consecutive terms have a constant ratio. So the ratio of the 2nd term to the 1st equals the ratio of the 3rd term to the 2nd. Concept: For a GP with terms a, b, c: b/a = c/b, so b² = ac. Solution: Terms: n − 2, n, n + 3 n/(n − 2) = (n + 3)/n Cross-multiply: n² = (n + 3)(n − 2) n² = n² + n − 6 0 = n − 6 n = 6 Terms: n − 2 = 4, n = 6, n + 3 = 9 Common ratio r = 6/4 = 3/2 Check: 9/6 = 3/2 ✓ Answer: The common ratio is 3/2, which is option A. Tip: Whenever you see three consecutive terms of a GP, use b² = ac right away. The n² terms cancel, leaving a simple linear equation. Always check by computing both ratios.AI can make mistakes. Report anything that looks wrong.
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