Question

設(shè)y=f(x)是一次函數(shù)，f(0)=1,且f(1),f(4),f(13)成等比數(shù)列，則=      。

Answer 1

n(2n+3)

由題意可設(shè)f(x)=kx+1,又f²(4)=f(1)f(13),得k=2.故f(x)="2x+1," f(2k)=4k+1.按等差數(shù)列求和，=" n(2n+3)" 。