If the G.P.’s 5, 10, 20, …. And 1280, 640, 320, … have their nth terms equal, find the value of n.

Question

Philoid · Accepted Answer

GP is given by

a, ar, ar², ⋯, arⁿ^-1

In the sequence 5, 10, 20, 40, …

First term, a = 5

Common ratio, r

Equate the term to be found with the nnth term.

arⁿ^-1=1280

5 × 2^n-1 =1280

2^n-1 = 256

n - 1 = 8

n =9

∴ 9^th term is equal.