Question

How do you find the sum of the geometric series `Sigma 5* 2^(n-1)` n=1 to 9?

Answer 1

Sum of first `9` terms is `2560`

Explanation:

In this geometric series first term `a_1=5.2^(1-1)=5*1=5` and common ratio `r` is `2`, as second term is `a_2=5.2^(2-1)=5*2=10` and `a_2/a_1=10/5=2`

The sum of such a series for first `n` terms is given by

`S_n=a_1xx(r^n-1)/(r-1)` and hence `S_n=5xx(2^n-1)/(2-1)`, as `a_1=5` and `r=2` and

Sum of first `9` terms is `5xx(2^9-1)/(2-1)=5xx512/1=2560`