(1/2) 在等差数列{an}中,若公差d≠0,a2是a1与a4的等比中项.已知数列a1·a3·ak·ak2·...akn·...成...

题目

(1/2) 在等差数列{an}中,若公差d≠0,a2是a1与a4的等比中项.已知数列a1·a3·ak·ak2·...akn·...成...
(1/2)
在等差数列{an}中,若公差d≠0,a2是a1与a4的等比中项.已知数列a1·a3·ak·ak2·...akn·...成等比数列

答案

an=a1+d(n-1)(a2)^2=(a1+d)^2=a1(a1+3d)a1=dan=dna1,a3,ak1,ak2,……,akn的公比q=a3/a1=3,k1=3*3=9akn/ak(n-1)=a3/a1=3即kn/k(n-1)=3kn=9*(1-3^n)/(1-3)=(9/2)*(3^n)-9/2