Answer: (B) -625
Step-by-step 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 [tex]\dfrac{-100}{-500}=\dfrac{1}{5}[/tex]
Input those values into the Sum formula:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_8=\dfrac{-500\bigg(1-\dfrac{1}{5}^n\bigg)}{1-\dfrac{1}{5}}\\\\.\quad=\dfrac{-500\bigg(1-\dfrac{1}{390,625}\bigg)}{\dfrac{4}{5}}\\\\.\quad=\dfrac{-500\bigg(\dfrac{390,624}{390,625}\bigg)}{\dfrac{4}{5}}\\\\.\quad=\dfrac{5(-500)(390,624)}{4(390,625)}\\\\.\quad=-624.998\\\\.\quad=-625\quad \text{(rounded to 2 decimal places)}[/tex]
