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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.
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Solution
Suppose the three terms of the geometric progression are `"a"/"r"`, a and ar.
Sum `"a"/"r" + "a" + "ar" = 39/10` ........(i)
And product = `"a"/"r" xx "a" xx "ar" = "a"^3 = 1`
or a = 1 ..........(ii)
By keeping a = 1 in equation (i)
`1/"r" + 1 + "r" = 39/10`
on multiplying by 10r
= 10 + 10r + 10r2 = 39r
= 10r2 − 29r + 10 =
= 10r2 - 25r - 4r + 10 = 0
= 5r (2r - 5) -2 (2r- 5) = 0
= (5r - 2) (2r - 5) = 0
r = `5/2` or `2/5`
a = 1
`1/"r" = 5/2, "r" = 2/5`
∴ Terms of geometric progression = `5/2, 1, 2/5` or `2/5, 1, 5/2`
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