设 $sed{a_k}_{k=1}^n$ 为等差数列, 则 $$ex a_1+cdots+a_n=frac{n(a_1+a_n)}{2}. eex$$ Ref. [Proof Without Words: Partial Sums of an Arithmetic Sequence, The College Mathematics Journal]. A visual proof that a partial sum of an arithmetic sequence equals the number of the terms times the average of the first and last term.