Question

Can somebody please please please give me a step by step answer for this question?

what is the sum of a 9 term geometric series if the first term is -11 and the common ratio is -4?

Answer 1

the sum of a geometric sequence is
if the first term is a and it is summed up to the nth term and r is the common ratio then

`S_n= (a(1-r^n))/(1-r)`
first term is -11 and the common ratio is -4 and n=9


`S_9= (-11(1-(-4)^9))/(1-(-4))`

`S_9= (-11(1-(-262144))/(1+4)`

`S_9= (-11(1+262144)/(5)`

`S_9= (-2883595)/(5)`

`S_9= -576719`