The formula that explain the arithmetic sequence is [tex]a_{n}=\frac{3}{7}n-\frac{9}{7}[/tex]
Step-by-step explanation:
The formula of the nth term in an arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
- a is the first term
- d is the common difference between the consecutive terms
∵ [tex]\frac{-6}{7}[/tex] , [tex]\frac{-3}{7}[/tex] , 0 , [tex]\frac{3}{7}[/tex] are some terms of an arithmetic sequence
∵ The difference between two consecutive terms = [tex]\frac{-3}{7}[/tex] - [tex]\frac{-6}{7}[/tex]
∴ The difference between two consecutive terms = [tex]\frac{-3}{7}[/tex] + [tex]\frac{6}{7}[/tex] = [tex]\frac{3}{7}[/tex]
∴ The common difference = [tex]\frac{3}{7}[/tex]
∴ d = [tex]\frac{3}{7}[/tex]
∵ The first term is [tex]\frac{-6}{7}[/tex]
∴ a = [tex]\frac{-6}{7}[/tex]
- Substitute a and d in the formula above
∴ [tex]a_{n}=\frac{-6}{7}+(n-1)\frac{3}{7}[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=\frac{-6}{7}+\frac{3}{7}n-\frac{3}{7}[/tex]
- Add like terms
∴ [tex]a_{n}=\frac{3}{7}n-\frac{9}{7}[/tex]
The formula that explain the arithmetic sequence is [tex]a_{n}=\frac{3}{7}n-\frac{9}{7}[/tex]
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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