Question

数学数列求前n项和相关题目{an}为等差数列,Sp=Sq,则Sp+q=?按等差求和公式怎么算啊.

Answer 1

Sp=p×a1+p(p-1)d/2

Sq=q×a1+q(q-1)d/2

由条件Sp=Sq

有pa1+p(p-1)d/2=q×a1+q(q-1)d/2

整理得:(p-q)a1=(q-p)(p+q-1)d/2

因为p≠q

所以a1=-(p+q-1)d/2

S(p+q)

=(p+q)a1+(p+q)(p+q-1)d/2

=-(p+q)(p+q-1)d/2+(p+q)(p+q-1)d/2

=0

Sp=p×a1+p(p-1)d/2 就是等差求和公式哦!

基本公式

Sp=a1+a2+...+ap

=a1+(a1+d)+(a1+2d)+...+[a1+(p-1)d]

=p×a1+[d+2d+...+(p-1)d]

=p×a1+[(1+p-1)(p-1)/2]d

=p×a1+(p-1)pd/2