The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
Step-by-step explanation:
The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex] , where
- a is the first term of the sequence
- r is the common ratio between each two consecutive terms
- [tex]r=\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex]
∵ The sequence is [tex]\frac{-2}{3}[/tex] , -4 , -24 , -144 , .......
∵ The 1st term is [tex]\frac{-2}{3}[/tex]
∵ The 2nd term is -4
∴ [tex]\frac{-4}{\frac{-2}{3}}=6[/tex]
∵ The 3rd term is -24
∴ [tex]\frac{-24}{-4}=6[/tex]
∵ The 4th term is -144
∴ [tex]\frac{-144}{-24}=6[/tex]
∵ [tex]\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex] = [tex]\frac{a_{4}}{a_{3}}[/tex] = 6
∴ There is a constant ratio between each two consecutive terms
∴ The sequence is a geometric sequence
∵ The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex]
∵ a = [tex]\frac{-2}{3}[/tex]
∵ r = 6
∴ The formula of the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
Learn more:
You can learn more about sequences in brainly.com/question/7221312
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