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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?

 Feb 7, 2020
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r = -1.5

a1 = 8000

 

 

Sum of a series ===    a1 (1-rn)/(1-r)

57875  = 8000 (1- (-1.5)n )/(1- -1.5)     now solve for n , the number of terms

57875 = 3200 (1-(-1.5)n )

           = 3200 - 3200(-1.5n)

54675 = -3200 (-1.5n)

-17.0859375 = (-1.5)n

n=7                                              to find the 7 th term   x7 = a1 (rn-1)  = 8000 (-1.5)= 91125

 Feb 7, 2020

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