The explicit formula for the geometric sequence [tex]c_{n}[/tex] is
[tex]c_{n}=6(\frac{-1}{3})^{n-1}[/tex]
Step-by-step explanation:
The formula of the nth term of a geometric sequence is
[tex]a_{n}=a(r)^{n-1}[/tex] , where:
The geometric sequence of [tex]c_{n}[/tex] is 6 , -2 , [tex]\frac{2}{3}[/tex] , [tex]\frac{-2}{9}[/tex] , [tex]\frac{2}{27}[/tex]
∵ [tex]c_{1}[/tex] = 6
∵ [tex]r=\frac{c_{2}}{c_{1}}[/tex]
∵ [tex]c_{2}[/tex] = -2
∴ [tex]r=\frac{-2}{6}[/tex]
- Divide both term by 2 to simplify it
∴ [tex]r=\frac{-1}{3}[/tex]
∵ [tex]c_{n}=c_{1}(r)^{n-1}[/tex]
- Substitute the value of [tex]c_{1}[/tex] and r in the rule above
∴ [tex]c_{n}=6(\frac{-1}{3})^{n-1}[/tex]
The explicit formula for the geometric sequence [tex]c_{n}[/tex] is
[tex]c_{n}=6(\frac{-1}{3})^{n-1}[/tex]
Learn more:
You can learn more about the geometric sequence in brainly.com/question/1522572
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