Question

SECTION A - Answer all the questions in this section. All questions carry equal marks.

Given that (7-2x), 9, (5x+17) are consecutive terms of a Geometric Progression (G.P) with common ratio, r>0, find the values of x.

Accepted Answer

For a G.P, the common ratio between consecutive terms is equal: 9/(7-2x) = (5x+17)/9.
Cross-multiplying: 81 = (7-2x)(5x+17) = 35x+119-10x^2-34x = -10x^2+x+119.
So 10x^2 - x + 81 - 119 = 0, i.e. 10x^2 - x - 38 = 0.
Using the quadratic formula or factorising: 10x^2+19x-38=0 factorises to give x = 2 or x = -19/10.
Since r>0, checking each value in the original terms, the valid answer is x = 2 (this keeps (7-2x)=3 and (5x+17)=27, giving common ratio r=9/3=3>0, consistent).

GCE Mathematics 2022 Theory — Question 1

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