sum of geometric sequence
for the sum where the initial value is a₁ and the common ratio is r and the term is n
\(S_n= \frac{a_1(1-r^n)}{1-r}\)
common ratio is -3
-5 times -3 is 15, -15 times -3=-45 etc
first term is -5
and we want the 8th term
\(S_8= \frac{-5(1-(-3)^8)}{1-(-3)}\)
\(S_8= \frac{-5(1-6561)}{1+3}\)
\(S_8= \frac{-5(-6560)}{4}\)
\(S_8= \frac{32800}{4}\)
\(S_8= 8200\)
the sum is 8200
