由a(n+1)=(5an-13)/(3an-7) --------1
得an = (7a(n+1) - 13) / (3a(n+1) - 5)
又a(n+2) = (5a(n+1)-13)/(3a(n+1)-7)
将公式1带入得
a(n+2) = (7an - 13) / (3an - 5) ---------2
由公式2得
a(n+3) = (7a(n+1) - 13) / (3a(n+1) - 5) = an
所以a(n+3) = an--------3
由公式1算得 a1=2 a2=3 a3=1
由公式3得
s100 = a1 + a2 + a3 + .+ a100
= (a1 + 12 + a3) .33 + a1 = 200