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# Two Quick Questions-I've Tried Already-Just A Little Stuck On Finding Series

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Hello, I've tried these problems out already, I'm just a little stuck. I appreciate all your help. Thanks.

(Also, if you can explain how you came up with the answer, that would also be great so that I can learn), Thanks much.

1.

What is the sum of the first eight terms of the series?

(−500)+(−100)+(−20)+(−4)+(−0.8)+...

Round the answer to two decimal places if necessary.

−996.09

−625

−624.99

−623

2.

What is the sum of the first 7 terms of the series  −3+6−12+24−... ?

Apr 9, 2018

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1. First eight terms  ..... (−500)+(−100)+(−20)+(−4)+(−0.8)+...

The common ratio is  (1/5)....the sum, S, is given by :

S  =  First Term  [  1 -  common ratio^8] / [ 1 - common ratio ]  =

S  =  -500  [  1  - (1/5)^8] / [ 1 - 1/5]   =  -[ 624  + 624/625 ]  ≈  -624.99

2.  What is the sum of the first 7 terms of the series  −3+6−12+24−... ?

The common ratio  is  -2

The sum, S, is given by :

S  =  -3  [ 1  - (-2)^7 ] / [  1 - (-2) ]   = -129

Apr 9, 2018