Question

Write an expression that gives the requested sum.

The sum of the first 16 terms of the geometric sequence with first term 9 and common ratio 2

Answer 1

The sum of the first 16 terms of the geometric sequence

`S_(16) = (9(2^(16)-1) )/(2-1)`

S₁₆ = 5,89,815

Step-by-step explanation:

Step-by-step explanation:-

Geometric series:-

The geometric sequence has its sequence Formation

a , a r, ar² , ar³,...…..a rⁿ be the n t h sequence

Given first term a=9 and common ratio 'r' = 2

The sum of the first 16 terms of the geometric sequence

`S_(n) = (a(r^(n)-1) )/(r-1) if r>1`

Given first term a=9 , 'r' = 2 and n=16

`S_(16) = (9(2^(16)-1) )/(2-1)`

`S_(16) = (9(2^(16)-1) )/(1)= 9(65,536-1)=5,89,815`