# 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

1 answer

###### 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

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

## Answers

Answer:The sum of the first 16 terms of the geometric sequence[tex]S_{16} = \frac{9(2^{16}-1) }{2-1}[/tex]S₁₆ = 5,89,815Step-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 sequenceGiven first term a=9 and common ratio 'r' = 2The 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]

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