The first term of a geometric sequence is 5 and the sixth term is 160. What is the common ratio?

Answer 1

First term in the geometric sequence: a = 5

n-th term T_n in the geometric sequence is given by the formula: T_n = ar^n-1 where r is the common ratio.

If we set n = 6, we get

T₆ = ar^6-1

It is given that the 6th term in the sequence is 160. Therefore T₆ = 160. So,

160 = 5r⁵

Divide both sides by 5 to get

32 = r⁵

Taking the 5th root of both sides, we get

(32)^1/5 = r

r = 2

Therefore, the common ratio is 2.