SEQUENCE AND SERIES A10

The 1st term of a geometric progression is 2 and the 5th term is 162. Find the common ratio.

Solution

G₁=2, G₅=162, n=5

G_n = G₁r^n-1;

G₅ = G₁r^5-1;

G₅ = G₁r⁴;

162 = 2 x r⁴;

162 = 2r⁴;

 2       2

81 = r⁴;  Finding the fourth root of 81,

r = 3

Hence the common ratio is 3.