How many terms reach a target?

You will find how many terms an arithmetic progression needs to reach a target, and recover the terms from a formula for the sum.

Your tasks.

1. In terms_to_reach, return the smallest $n$ for which the sum of the first $n$ terms is at least target. The common difference is positive.
2. In nth_term_from_sum, return the $n$th term, $S(n) - S(n - 1)$, from a function S that gives the sum of the first $n$ terms.
3. Set term_12 to the $12$th term of the progression whose sum of $n$ terms is $3n^2 + 2n$.