WAEC 2020 Mathematics · Question 13

The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio.

Options

A.2
B.4
C.8
D.16

Answer: A. 2

Explanation written with AI and checked against the answer key

Analyze the question: We're given a G.P. with first term a = 3 and 5th term T₅ = 48. We need the common ratio r. Concept: The nth term of a G.P. is Tₙ = arⁿ⁻¹ Solution: T₅ = ar⁴ 3 × r⁴ = 48 r⁴ = 48 ÷ 3 = 16 r⁴ = 2⁴ r = 2 (taking the positive real value) Note: r = −2 also satisfies r⁴ = 16, but −2 is not among the options, so the answer is 2. Check: 3, 6, 12, 24, 48. The 5th term is 48 ✓. Answer: A. 2 Tip: For the 5th term, the power of r is 4 (one less than the term number). When you get rⁿ = a number, try to write that number as a power with the same index, as we did with 16 = 2⁴. Always verify by listing out the terms.

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