SEQUENCE AND SERIES A3

The 1st term of a geometric progression is 3 and the 6th term is 96. Find the common ratio.

Solution

G₁=3, G₆=96, n=6

G_n = G₁r^n-1;

G₆ = G₁r^6-1;

G₆ = G₁r⁵;

96 = 3 x r⁵;

96 = 3r⁵;

 3     3

32 = r⁵;  Finding the fifth root of 32,

r = 2

Hence the common ratio is 2.