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?

jjennylove Mar 18, 2019

#1**+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

CPhill Mar 18, 2019