find the number of terms in the geometric sequence 51020320S

find the number of terms in the geometric sequence 5,10,20,...,320

Solution

5,10,20,...,320

Its a G.P. series as common ration = 10/5 = 20/10 ----

r = 2

nth term : an = a1r^n-1

320 = 5(r)^n-1

320 = 5(2)^n-1

64 = 2^n-1

2^6 = 2^(n-1)

n-1 = 6

n = 7 terms