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Question
Find the sum of first n terms of the G.P.
`5, -3, 9/5, - 27/25, ...`
Solution
`5, -3, 9/5, - 27/25, ...`
Here a = 5, r = `("t"_2)/("t"_1) = (-3)/5 < 1`
Sn = `"a"[(1 - "r"^"n")/(1 - "r")]`
= `5[(1 - ((-3)/5)^"n")/(1 - ((-3)/5))]`
= `5[(1 - ((-3)/5)^"n")/(1 - (-3)/5)]`
= `5 ([1 - ((-3)/5)^"n"])/(8/5)`
= `5 xx 5/8[1 - ((-3)/5)^"n"]`
∴ Sn = `25/8[1 - ((-3)/5)^"n"]`
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