Question

设公差为非零的等差数列{An}与等比数列{Bn},满足A1=B1,A3=B3,A7=B5,试问对怎样的n,m,可使An=

Answer 1

设An=A1+(n-1)d

Bm=B1*q^m

因为A1=B1;A3=B3;A7=B5

则可得

A1(1-q^2)=2d

A1(1-q^4)=6d

比得

q^4-3q^2+2=0

(q^2-1)(q^2-2)=0

且2d=A1(q^2-1)

因为公差不为零,所以q^2=2,

d=A1/2

带入An=Bm

可得:A1+(n-1)(A1/2)=A1*q^(m-1)

化简1/2*(1+n)= q^(m-1)即可解得