Question

How do you find the formula for `a_n` for the arithmetic sequence `a_1=-y, d=5y`?

Answer 1

`u_n = (5n-6)y`

Explanation:

If we have `n` terms of an AP, with first term `a`, and common difference `d` the terms are:

`{a,a+d,a+2d,...,a+(n-1)d}`

Assuming `a_1` is the first term (as opposed to `a_0`) then we have:

`a = -y`
`d = 5y`

So the `n^(th)` term us:

`u_n = -y + (n-1)5y`
`\ \ \ \ = (5n-6)y`