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The sum of a geometric series whose first three terms are 8000, -12000, and 18000 is 57875. What is the last term of the series?

 Jan 26, 2019
 #1
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The common ratio is -1.5

 

To find the number of terms, we have

 

57875 =  8000 [ 1 - (-1.5)^n ]   / [  1 - (-1.5) ]

 

57875 = 3200 [ 1 - (-1.5)^n ] 

 

2315/128 = 1 - (-1.5)^n

 

(-1.5)^n =  1 - 2315/128

 

(-1.5)^n = -2187/128       n must be odd.....so....we can solve this

 

1.5^n =  2187/128     take the log of both sides

 

n log 1.5 =  log (2187/128)

 

n =    log(2187/128) / log (1.5)   =  7

 

So....we are looking for the 7th term which is

 

8000(-1.5)^(7 - 1)  =   91125

 

 

cool cool cool

 Jan 26, 2019

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