bellambernal2003
Answered

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Find the sum of the first n terms
using the formula:
a(1-rn)
1-r
85 +85(.9) +85(.9)² + ...
. (5 terms)

Sagot :

The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.

What is the sum of terms of a geometric sequence?

Let's suppose its initial term is a , multiplication factor is  r and let it has total n terms,

then, its sum is given as:

[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

Given geometric sequence;

85 +85(.9) +85(.9)² + ...

a = 85

r = 0.9

its sum is given as:

[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]

[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]

Thus,

The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.

Learn more about geometric sequence here:

https://brainly.com/question/2735005

#SPJ1

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