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_数学解答

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

人气：201 ℃　时间：2019-10-14 05:59:46

解答

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) a^2 + 3a - 10 = (a+5)(a-2),
-5 < a = a(1) < 2.