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The First Term of a G.P is 27 and Its 8th Term is 1/81 Find the Sum of Its First 10 Terms. - Mathematics

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
8th term = ar7 = `1/81`

n = 10
Now,

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

⇒ r7 = `1/2187`

⇒ r7 = `(1/3)^7`

⇒ r = `1/3` (r < 1)

∴ Sn =`(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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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 3 | Page 161
Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 18 | Page 161
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