等差数列各项平方的和怎么算?

题目

等差数列各项平方的和怎么算?

答案

首项a1,公差d的等差数列各项平方的和
=a1²+(a1+d)²+(a1+2d)²+--------+[a1+(n-1)d]²
=na1²+[2+4+6+-------+2(n-1)]d+[1²+2²+3²+-----+(n-1)²]d²
=na1²+n(n-1)d+n(n-1)(2n-1)d²