Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

What is the sum of the first eight terms of the series?

(−500) + (−100) + (−20) + (−4) + (−0.8) + ...



Round the answer to two decimal places if necessary.

Answer 1

Answer: (B) -625

Explanation:

Given the sequence {-500, -100, -20, -4, -0.8, ... }, we know that that the first term (a) is -500 and the ratio (r) is
`(-100)/(-500)=(1)/(5)`

Input those values into the Sum formula:

`S_n=(a(1-r^n))/(1-r)\\\\S_8=(-500\bigg(1-(1)/(5)^n\bigg))/(1-(1)/(5))\\\\.\quad=(-500\bigg(1-(1)/(390,625)\bigg))/((4)/(5))\\\\.\quad=(-500\bigg((390,624)/(390,625)\bigg))/((4)/(5))\\\\.\quad=(5(-500)(390,624))/(4(390,625))\\\\.\quad=-624.998\\\\.\quad=-625\quad \text{(rounded to 2 decimal places)}`