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salantis [7]
3 years ago
9

-6/7,-3/7,0,3/7 .... create a formula that explains the arithmetic sequence

Mathematics
1 answer:
LenKa [72]3 years ago
3 0

The formula that explain the arithmetic sequence is a_{n}=\frac{3}{7}n-\frac{9}{7}

Step-by-step explanation:

The formula of the nth term in an arithmetic sequence is

a_{n}=a+(n-1)d , where

  • a is the first term
  • d is the common difference between the consecutive terms

∵ \frac{-6}{7} , \frac{-3}{7} , 0 , \frac{3}{7} are some terms of an arithmetic sequence

∵ The difference between two consecutive terms = \frac{-3}{7} - \frac{-6}{7}

∴ The difference between two consecutive terms = \frac{-3}{7} + \frac{6}{7} = \frac{3}{7}

∴ The common difference = \frac{3}{7}

∴ d = \frac{3}{7}

∵ The first term is \frac{-6}{7}

∴ a = \frac{-6}{7}

- Substitute a and d in the formula above

∴ a_{n}=\frac{-6}{7}+(n-1)\frac{3}{7}

- Simplify the right hand side

∴ a_{n}=\frac{-6}{7}+\frac{3}{7}n-\frac{3}{7}

- Add like terms

∴ a_{n}=\frac{3}{7}n-\frac{9}{7}

The formula that explain the arithmetic sequence is a_{n}=\frac{3}{7}n-\frac{9}{7}

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

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