Question

The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratio and the terms.​

Answer 1

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Let the three terms of the GP be a/r, a and ar.

Their product = a³ = 1 or a = 1

Their sum is (1/r)+1+(1×r) = (1+r+r²)/r = 39/10, or

10(1+r+r²) = 39r, or

10r² +10r-39r+10 = 0, or

10r²–29r+10 = 0, or

10r²–25r-4r+10 = 0

5r(2r-5) -2(2r-5) = 0, or

(5r-2)(2r-5) = 0, or

r = 2/5 or 5/2.

So the first three terms of the GP are 5/2, 1, and 2/5, or

2/5, 1, 5/2. The common ratio is 2/5 or 5/2.