呀呀呀~~看这里~~等差数列~~简单题一道啊~~~

来源：百度知道 编辑：UC知道 时间：2024/06/21 09:09:39
在等差数列{an}中,Sp=q Sq=P 则Sp+q的值为?

Sp=a1p+p(p-1)d/2=q (1)
Sq=a1q+q(q-1)d/2=p (2)
(1)-(2)
a1(p-q)+(p+q-1)(p-q)d/2=q-p
a1+(p+q-1)d/2=-1
a1=-1-(p+q-1)d/2
Sp+q=a1(p+q)+(p+q)(p+q-1)d/2
=[-1-(p+q-1)d/2](p+q)+(p+q)(p+q-1)d/2
=-(p+q)

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

Sp=Sq
所以,pa1+p*(p-1)*d/2=qa1+q*(q-1)*d/2
化简,得:(p-q)*a1=(q-p)*(p+q-1)*d/2
1
若p≠q
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

2
若p=q
无解！