Question

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?

Answer 1

Sum`=-547.`

Explanation:

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

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

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

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