Question

Given `a_17=-82, d=-3`, how do you find `a_24`?

Answer 1

`a_24 = -93`

Explanation:

Find the first element of the sequence using the formula for arithmetic sequences: `a_n = a_1 + (n-1)d`

`a_17 = -82 = a_1 + (17-1)(-3)`
`-82 = a_1 + 16(-3)`
`-82 = a_1 -48`
`-82+48 = a_1 -48+48`
`a_1 = -82 + 48`
`a_1 = -24`

Now use the arithmetic sequence formula to find `a_24`:

`a_24 = -24 + (24-1)(-3)`
`a_24 = -24 + (23)(-3)`
`a_24 = -24 -69`
`a_24 = -93`