在等比数列{an}和等差数列{bn}中,a1=b1>0,a3=b3>0,a1不等于a3,试比较a5和b5的大小

a1+a5=2a3,a5=2a3-a1;
b1*b5=b3^2,b5=b3^2/b1;
且a1=b1>0,a3=b3>0,a1不等于a3
a5-b5=2a3-a1-b3^2/b1
=2a3-a1-a3^2/a1
=（2a3a1-a1^2-a3^2）/a1
=-（a1-a3）^2/a1
<0
所以a5<b5

a(n) = aq^(n-1),
b(n) = b + r(n-1), n = 1,2,...

a(1) = a = b(1) = b > 0.
a(3) = aq^2 = b(3) = a + 2r, 2r = a(q^2 - 1).
a(3) = aq^2 不等于a(1) = a, q^2不等于1.
r = a(q^2-1)/2.

b(5) = a + 4r = a + 2a(q^2-1) = a[2q^2-1]
a(5) = aq^4 = aq^4
a(5) - b(5) = a[q^4 - 2q^2 + 1] = a[q^2 - 1]^2 > 0
a(5) > b(5).