SOLUTION: The sum of a geometric sequence 2 - 6 + 18 - 54 + ... - tn is - 29 524. Find the number of terms.

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Question 1202480: The sum of a geometric sequence 2 - 6 + 18 - 54 + ... - tn is - 29 524. Find the number of terms.
Answer by ikleyn(52787) About Me  (Show Source):
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The sum of a geometric sequence 2 - 6 + 18 - 54 + ... - tn is - 29524.
Find the number of terms.
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This geometric progression has the first term a= 2 and the common ratio -3.


Use the general formula for the sum of the first n terms

    S%5Bn%5D = a%2A%28%28r%5En-1%29%2F%28r-1%29%29.


It gives

    -29524 = 2%2A%28%28%28-3%29%5En-1%29%2F%28%28-3%29-1%29%29.


Simplify and find n

    %28%28-29524%29%2A%28-4%29%29%2F2 = %28-3%29%5En-1

    59048 = %28-3%29%5En-1

    59048 + 1 = %28-3%29%5En

    59049 = %28-3%29%5En

    %28-3%29%5E10 = %28-3%29%5En


It implies  n= 10.


ANSWER.  The number of terms is 10.

Solved.