How do you find the sum of the first 7 terms of a geometric sequence if the first term is -1 and the common ratio is -3?

1 Answer
Ratnaker Mehta
Jul 10, 2016

Sum=-547.=−547.

Explanation:

Let, S_n=Sn= the sum of first n terms, a=a= the first Term, and, r=r=the common ratio of the Geometric seq., where, a!=0, |r|!=1.a≠0,|r|≠1.

Then, S_n=a*{(r)^n-1}/(r-1)Sn=a⋅(r)n−1r−1

In our case, n=7, a=-1, r=-3n=7,a=−1,r=−3

:. S_7=-{(-3)^7-1}/(-3-1)=((-2187-1)/4=-2188/4=-547.

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