Question

Write an expression that gives the requested sum.

Answer 1

Answer:

The sum of the first 16 terms of the geometric sequence

$S_{16} = \frac{9(2^{16}-1) }{2-1}$

S₁₆ = 5,89,815

Step-by-step explanation:

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

$S_{n} = \frac{a(r^{n}-1) }{r-1} if r>1$

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

$S_{16} = \frac{9(2^{16}-1) }{2-1}$

$S_{16} = \frac{9(2^{16}-1) }{1}= 9(65,536-1)=5,89,815$