Question

How do you find a general formula for each arithmetic sequence given 8th term is -20; 17th term is -47?

Answer 1

`n^(th)` term of the arithmetic sequence is given by `4-3n`

Explanation:

If `a` is the first term of an arithmetic sequence and `d` the difference between a term and its preceding term, general formula for `n^(th)` term of the arithmetic sequence is given by `a+(n-1)d`.

As `8^(th)` term is `-20` and `17^th` term is `-47`

`a+(8-1)d=a+7d=-20` and `a+(17-1)d=a+16d=-47`.

Subtracting first equation from second, we get

`9d=-47+20` or `9d=-27` i.e. `d=-3`

putting this in first we get `a+7*(-3)=-20` or `a=1`.

Hence, `n^(th)` term of the arithmetic sequence is given by `1-3(n-1)` or `4-3n`