设正项数列｛an}是公差不为零的等差数列,正项数列{bn}是等比数列,且a1=b1,a3=b3,a7=b5

题目

设正项数列｛an}是公差不为零的等差数列,正项数列{bn}是等比数列,且a1=b1,a3=b3,a7=b5
求公比q
b7是不是在an上

答案

a3=b3a1+2d=b1*q^2=a1*q^ 2a1+2d=a1*q^ 2.1a7=b5a1+6d=b1*q^4=a1*q^4a1+6d=a1*q^4.21式×3-2式2a1=3a1*q^2-a1q^43q^2-q^4=2q^4-3q^2+2=0(q^2-2)(q^2-1)=0则q^2=1或q^2=2又｛an｝是正项数列,｛bn｝是正项数列所以q=1...