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?

noobieatmath Jan 26, 2019

#1**+1 **

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

CPhill Jan 26, 2019