令d为公差
an+am=a1+(n-1)d+a1+(m-1)d
=2a1+(n+m-2)d
ap+aq=a1+(p-1)d+a1+(q-1)d
=2a1+(p+q-2)d
因为：m+n=p+q(m、n、p、q属于N)
所以：an+am=ap+aq.