Question

已知数列an满足An=2n+1/5n²-3,求a₁,A2n+1.

Answer 1

An代表什么?是否前n项和Sn?

An=(2n+1)/(5n^2-3), a1=A1=3/2,

A2n+1=[2(2n+1)+1]/[5(2n+1)^2-3]=(4n+3)/(20n^2+20n+2).

a1=2, A2=2A1+3=2a1+3=7, a2=7-2=5, A3=2*7+3=17, a3=17-7=10,

A4=2*17+3=37, a4=37-17=20, A5=2*37+3=77, a5=77-37=40.

a27=a1+26d, 54=20+26d, d=17/13.

a10,a20,a30 成等差数列,a10+a30=2a20,20+a30=2*10,a30=0.

an=(1/4)2^n=(1/2)2^(n-1), a1=1/2, q=2.