Question

How many terms are there in a geometric series if the first term is 3, the common ratio is 4 and the sum of the series is 1,023

Answer 1

The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) in our case:

s(n)=3(1-4^n)/(1-4)

s(n)=-(1-4^n)

s(n)=(4^n)-1 and s=1023

(4^n)-1=1023

4^n=1024

n ln4=ln1024

n=(ln1024)/(ln4)

n=5