Question

已知等差数列｛an｝的公差d＝1+前n项和为sn，若1,a1,a3成等比数列求a1

若s5＞a1a9求a1的范围

Answer 1

a(n) = a + (n-1),
a(1)=a,
[a(1)]^2 = a^2 = 1*a(3) = a+2,
0 = a^2 - a - 2 = (a-2)(a+1),
a(1) = a = 2或a(1) = a = -1.

s(n) = na + n(n-1)/2,
a(1)a(9) = a(a+8)<s(5) = 5a+10,
0 > a^2 + 3a - 10 = (a+5)(a-2),
-5 < a = a(1) < 2.