The sum of the first five terms of the geometric series 8, -24, 72..... is 488 ⇒ answer B
Step-by-step explanation:
In the geometric series:
∵ 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 488
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