等差数列{an}中ap=1997a1997=o

Question

等差数列{an}中ap=1997 a1997=o

Answer 1

∵是等差数列
所以根据ap=q,aq=p可以算出公差d
若paq=ap+(q-p)*d
∴d=(aq-ap)/(q-p)=(p-q)/(q-p)=-1
∴a(p+q)=ap+(p+q-p)*d=ap+q*d=q-q=0
若p>q
ap=aq+(p-q)*d
∴(ap-aq)/(p-q)=(q-p)/(p-q)=-1
∴a(p+q)=aq+(p+q-q)*d=aq+p*d=p-p=0
综上所述a(p+q)=0