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

Question

Philoid · Accepted Answer

Given: G.P. 3, 3², 3³, … 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

⇒ 3ⁿ = 80 +1 = 81

⇒ 3ⁿ = 81

Applying ln on both sides, we get

⇒

⇒ n = 4

How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?