An AP toolkit

You will write three small functions for arithmetic progressions: the $n$th term, the sum of $n$ terms, and the means between two numbers. The checker tests them on many cases.

The idea. $a_n = a + (n - 1)d$, $S_n = \dfrac{n}{2}\left(2a + (n - 1)d\right)$, and $m$ means between $x$ and $y$ step by $\dfrac{y - x}{m + 1}$.

Your tasks.

1. Finish nth_term(a, d, n).
2. Finish ap_sum(a, d, n). Use / 2 and return the number it gives.
3. Finish means(x, y, m): return the list of the $m$ means, in order.