Question

How do you find the formula for `a_n` for the arithmetic sequence `10, 5, 0, -5, -10, ...`?

Answer 1

`a_n = 15 - 5n`

Explanation:

We know the first term and the common difference.

`t_n = a + (n - 1)d`

`t_n = 10 + (n - 1)-5`

`t_n = 10 - 5n + 5`

`t_n = 15 - 5n`

Note that `a_n` and `t_n` are equivalent terms.

Hopefully this helps!