The second term of a geometric sequence is 18, and the sixth term is 288. Find the nth term. (Assume that the terms of the sequence are positive.)

Question

Answer 1

a2 = 18

a6 = 288

an = a1(r^(n-1))

a2 = a1(r)= 18

a6 = a1(r^5) = 288

divide last equation by 2nd to last equation

r^4 = 288/18 = 16

r^2 = 4

r = 2 = common ratio

a2 = a1(r) = 2a1 = 18

a1 = 18/2 = 9

an = 9(2^(n-1))

a6=9(2^5) = 9(32) = 288

a2 = 9(2^1) = 18