Question

For a GP, a is 5 and r is 2. The sum of a certain number of terms of this GP is 315. Find the number of terms

Answer 1

Answer:

given : in a G.P, a = 5 , r = 2, Sₙ = 315

to find , number of terms n

formula used, Sₙ = [a(rⁿ - 1)] / (r - 1) [ | r | > 1 ]

=> 315 = 5 ( 2ⁿ - 1)/2-1

=> 315 = 5 ( 2ⁿ - 1)

=> 2ⁿ - 1 = 315/5 = 63

=> 2ⁿ = 63 +1 = 64

=> 2ⁿ = 2⁶

=> n = 6

therefore number of terms is 6