The sum of the first 8 terms is 2.51 to the nearest hundredth
Step-by-step explanation:
In the geometric sequence there is a constant ratio between each two consecutive terms
The formula of the sum of n terms of a geometric sequence is:
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex] , where
∵ The sequence is 6 , -5 , 25/6 , .............
∵ -5 ÷ 6 = [tex]\frac{-5}{6}[/tex]
∵ [tex]\frac{25}{6}[/tex] ÷ -5 = [tex]\frac{-5}{6}[/tex]
- There is a constant ratio between the consecutive terms
∴ The sequence is a geometric sequence
∵ The first term is 6
∴ a = 6
∵ The constant ratio is [tex]\frac{-5}{6}[/tex]
∴ r = [tex]\frac{-5}{6}[/tex]
∵ We need to find the sum of 8 terms
∴ n = 8
- Substitute the values of a, r and n in the rule above
∴ [tex]S_{8}=\frac{6[1-(\frac{-5}{6})^{8}]}{1-(\frac{-5}{6})}[/tex]
∴ [tex]S_{8}=2.511595508[/tex]
- Round it to the nearest hundredth
∴ [tex]S_{8}=2.51[/tex]
The sum of the first 8 terms is 2.51 to the nearest hundredth
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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