Q. 134.1( 41 Votes )

# How many terms of G.P. 3, 3^{2}, 3^{3}, … are needed to give the sum 120?

Answer :

Given: G.P. 3, 3^{2}, 3^{3}, … and Sum = 120

Here a = 3 and r = = 3

The Sum of terms in G.P. is given by:

∴ = 120

⇒ = 120

⇒ = 120(2)

⇒ = 240

⇒ = = 80

⇒ 3^{n} = 80 +1 = 81

⇒ 3^{n} = 81

Applying ln on both sides, we get

⇒

⇒

⇒ n = 4

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