The first term of an arithmetic progression is 3 and the 5th term is 9.find the number of term in the progression if the last term is 81.
a=3
ar^4 = 9
3r^4 = 9
r^4 = 3
r = 3^(1/4)
ar^(n-1) = 81
3 (3^(1/4) )^(n-1) = 3^4
3^(1/4) )^(n-1) = 3^3
3((n/4 - 1/4) = 3^3
n/4 - 1/4 = 3
n - 1 = 12
n = 13 < ------ number of terms