等差数列{an}中.S9=-18,S13==-52,等比数列{bn}中b5=a5,b7=a7,则b19,b1的几何平均数?

解,等差数列
S9 = 9(a1 + a9 )/2 =9a5 =-18
S13 = 13(a1+a13)/2 =13a7=-52
所以,a5=-2,
a7=-4
等比数列{bn}中b5=a5,b7=a7,则
q^2=b7/b5=a7/a5=2
b5=b1q^4=-4b1=-2,则b1=-1/2
b19,b1的几何平均数= 根号b19xb1=根号b1^2xq^18=根号1/4 x 2^9= 根号2^7=8*根号下2.