Question

How do you write the nth term rule for the arithmetic sequence with `d=5/3` and `a_8=24`?

Answer 1

`a_n = 1/3(32+5n)`

Explanation:

The `n^(th)` term of an arithmetic sequence in terms of the `m^(th)` term and the common difference `(d)` is given by:

`a_n = a_m + (n-m)d`
In this example; `m=8, d=5/3` and `a_8 = 24`

Replacing these values into the general formula above`->`
`a_n = a_8+(n-8)*5/3`

`a_n = 24+(n-8)*5/3`
`=1/3(72+5n-40)`

`=1/3(32+5n)`