Question

Find the sum of the first n terms

Answer 1

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:

$S_n = \dfra$$\dfrac{a(r^n-1)}{r-1}$

(sum till nth term)

Given geometric sequence;

85 +85(.9) +85(.9)² + ...

a = 85

r = 0.9

its sum is given as:

$S_n = \dfra$$\dfrac{a(r^n-1)}{r-1}$

$S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08$

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:

brainly.com/question/2735005

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