Find the sum of the first five terms of the geometric series 8, -24, 72.....A) 484B) 488C) 648D)684

The sum of the first five terms of the geometric series 8, -24, 72..... is 488 ⇒ answer BStep-by-step explanation:In the geometric series:There is a constant ratio " r " between each two consecutive termsThe nth term is [tex]a_{n}=ar^{n-1}[/tex] , where a is the 1st termThe sum of nth terms is [tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]∵ 8 , -24 , 72 , ........ is a geometric series∵ [tex]r=\frac{a_{2}}{a_{1}}[/tex]∵ [tex]a_{1}[/tex] = 8∵ [tex]a_{2}[/tex] = -24∴ [tex]r=\frac{-24}{8}[/tex]∴ r = -3∵ The sum of the nth terms is [tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]- We need the sum of the first 5 terms, then n is 5∵ n = 5 , a = 8 , r = -3- Substitute these values in the rule of the sum∴ [tex]S_{5}=\frac{8(1-(-3)^{5})}{1-(-3)}[/tex]∴ [tex]S_{5}=\frac{8(1-(-243))}{1+3}[/tex]∴ [tex]S_{5}=\frac{8(1+243)}{4}[/tex]∴ [tex]S_{5}=\frac{8(244)}{4}[/tex]∴ [tex]S_{5}=488[/tex]The sum of the first five terms of the geometric series 8, -24, 72..... is 488Learn more:You can learn more about sequence in brainly.com/question/1522572#LearnwithBrainly