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

$S_n= \frac{a_1(1-r^n)}{1-r}$

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