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I need help with this practice problem ****If you can, show your work step by step

I need help with this practice problem ****If you can, show your work step by step-example-1
User Nam Lee
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1 Answer

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The given series is expressed as

120 - 80 + 160/3 - 320/9 + ....

Given that it is a geometric series, it means that the consecutive terms have a common ratio, r. We have

r = - 80/120 = (160/3)/- 80 = (- 320/9)/(160/3) = - 2/3

The formula for calculating the sum of n terms in a geometric series, Sn is expressed as

Sn = a(1 - r^n)/(1 - r)

where

a is the first term

n is the number of terms

From the information given,

a = 120

r = - 2/3

n = 8

We want to find S8. It becomes

S8 = 120(1 - (- 2/3)^8/(1 - - 2/3)

S8 = 120(1 - - 256/6561)/(1 + 2/3)

S8 = 120(1 + 256/6561)/(5/3)

S8 = 120(6817/6561)/(5/3)

S8 = 120(6817/6561)(3/5)

S8 = 50440/729

The sum of the first 8 terms is 50440/729

User Tmont
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