Answer:
The sum of the first 16 terms of the geometric sequence
[tex]S_{16} = \frac{9(2^{16}-1) }{2-1}[/tex]
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
[tex]S_{n} = \frac{a(r^{n}-1) }{r-1} if r>1[/tex]
Given first term a=9 , 'r' = 2 and n=16
[tex]S_{16} = \frac{9(2^{16}-1) }{2-1}[/tex]
[tex]S_{16} = \frac{9(2^{16}-1) }{1}= 9(65,536-1)=5,89,815[/tex]
