Sum

The first term of a G.P is 27 and its 8th term is `1/81` Find the sum of its first 10 terms.

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#### Solution

Given ,

First term, a = 27

8^{th} term = ar^{7} = `1/81`

n = 10

Now,

`"ar"^7/"a"=(1/81)/27`

⇒ r^{7} = `1/2187`

⇒ r^{7} = `(1/3)^7`

⇒ r = `1/3` (r < 1)

∴ S_{n} =`(a(1-r^n))/(1-r)`

`=> "S"_10=(27(1-(1/3)^10))/(1-1/3)`

`=(27(1-1/3^10))/(2/3)`

`=81/2(1-1/3^10)`

`= 81/2 (1 - 3^(-10))`

Concept: Geometric Progression - Finding Sum of Their First ‘N’ Terms

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