Question

若{An}是等差数列,证明Ak,Ak+m,Ak+2m仍成等差数列

Answer 1

ak=a1+(k-1)d

a(k+m)=a1+(k+m-1)d

a(k+2m)=a1+(k+2m-1)d

2a(k+m)=2a1+2(k+m-1)d

ak+a(k+2m)=a1+(k-1)d+a1+(k+2m-1)d

=2a1+(k-1+k+2m-1)d

=2a1+(2k+2m-2)d

=2a1+2(k+m-1)d

=2a(k+m)

所以ak,a(k+m),a(k+2m)仍成等差数列