+148 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?
+129852 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
