Question

Find the sum of the first 8 terms of the sequence: -5. 15, -45, 135, .......

Answer 1

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= (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= (-5(1-(-3)^8))/(1-(-3))`

`S_8= (-5(1-6561))/(1+3)`

`S_8= (-5(-6560))/(4)`

`S_8= (32800)/(4)`

`S_8= 8200`


the sum is 8200