Question

已知{an}是公差为d的等差数列,{bn}是公比是q的等比数列,找出所有数列{an},{bn},使得对一切n属于N*,a

Answer 1

由a/an=bn,得

a/a=b,

{an}是公差为d的等差数列,{bn}是公比是q的等比数列,

∴a/a*an/a=q,

即[a1+(n-1)d][a1+(n+1)d]/[a1+nd]^2=q(常数）对n∈N*都成立,

∴d=0,q=1.

∴an=a1≠0,bn=1.