# 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.

#### 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