Need help with this question

Question

What is sum of the geometric sequence -3, 18, -108... If there are 8 terms?

Answer 1

The formula for the sum of a geometric series is (a - arⁿ)/(1-r) where a is the first term, r is the ratio, and n is the number of terms.

In the example, the first term is -3, so a is -3.  The ratio is 18/-3 = -6.  There are 8 terms.  Thus, the sum is

(-3 - -3 * (-6)⁸ ) / (1 - (-6)) = (-3 + 3 * 1679616)/7 = (-3 + 5038848)/7 = 719835

 

You could also easily write all terms in Excel by making each term = -6*the previous term, getting the first 8 terms, and adding.