Question

等差数列｛a｝的公差d≠0,它的部分项依次组成的数列Ak1,Ak2,…Akn成等比数列,其中k1=1,k2=5,k3=1

Answer 1

设等差数列第一项为a1,公差d,

ak1=a1,ak2=a1+4d,ak3=a1+16d;

因为等比,ak1*ak3=ak2*ak2,

解得,a1=2d,

ak1=2d,ak2=6d,ak3=18d,公比q=3;

得：akn=2d*3^(n-1);

kn=2*3^(n-1)-1;