Question 20
Let $n \ge 2$ be an integer and let $a_0, a_1, \ldots, a_n$ be consecutive terms of an arithmetic progression. Prove that
$$
a_0 - \binom{n}{1}a_1 + \dots + (-1)^k \binom{n}{k}a_k + \dots + (-1)^n \binom{n}{n}a_n = 0.
$$
$$
a_0 - \binom{n}{1}a_1 + \dots + (-1)^k \binom{n}{k}a_k + \dots + (-1)^n \binom{n}{n}a_n = 0.
$$