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avatar+976 

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

 Wouldn't it be -625 rounded to the 2 decimal places?

 Mar 18, 2019
 #1
avatar+102409 
+1

The common ratio is   -100/-500 =   1/5  = r

 

The sum, S,  of the first n terms is given by

 

S =    first term [ 1 - common ratio ^(n - 1) ] / [ 1 - r ]

 

So...the sum of the first 8 terms is

 

S  = (-500) [ 1 - (1/5)^(8 - 1) ]  / [ 1 - 1/5]    =

 

(- 500 ) [ 1 - (1/5)^7 ] / [ (4/5) ]  =  -624.992

 

Rounding to 2 decimal places.....note that the third decimal place is < 5

 

So....we round to     -624.99

 

cool cool cool

 Mar 18, 2019
 #2
avatar+976 
0

it was actually -625 but thank you for your help

jjennylove  Mar 18, 2019

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