A_n = a_1 + a_1 + d + a_1 + 2d  + \cdots + a_1 + (n-2)d + a_1 +(n-1)d = n \cdot a_n + \biggl(1+2+\cdots + (n-2) + (n-1)\biggr)d = n \cdot a_1 + \frac{(n-1)n}{2}d = \frac{n}{2}\biggl(2a_1 + (n-1)d\biggr)