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Mathematics

Find the sum of first 8 terms of the G.P. 1, 3, 9, 27, 81, …..

G.P.

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Answer

Given,

a = 1

r = 31\dfrac{3}{1} = 3

n = 8

We know that,

The sum of the first n terms of a G.P. is given by :

Sn=a(rn−1)r−1S_n = \dfrac{a(r^n - 1)}{r - 1} [For r > 1]

Substituting values we get :

⇒S8=1(38−1)3−1=38−12=6561−12=65602=3280.\Rightarrow S_8 = \dfrac{1(3^8 - 1)}{3 - 1} \\[1em] = \dfrac{3^8 - 1}{2} \\[1em] = \dfrac{6561 - 1}{2} \\[1em] = \dfrac{6560}{2} \\[1em] = 3280.

Hence, S8 = 3280.

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