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