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Question
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to ______.
Options
1 : 1
(Common ratio)n : 1
(First term)2 : (Common ratio)2
None of these
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Solution
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to 1 : 1.
Explanation:
Let us take a G.P. with three terms `a/r, a, ar`.
Then S = `a/r + a + ar = (a(r^2 + r + 1))/r`
P = a3
R = `r/a + 1/a + 1/ar`
= `1/a((r^2 + r + 1)/r)`
`(P^2R^3)/"S"^3 = (a^6 * 11/a^3 ((r^2 + r + 1)/r)^3)/(a^3((r^2 + r + 1)/r)^3` = 1
Therefore, the ratio is 1 : 1
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