已知数列{an},{bn},{an}为公比q>0的等比数列,Sn,Tn分别为{an},{bn}的前n项和

题目

已知数列{an},{bn},{an}为公比q>0的等比数列,Sn,Tn分别为{an},{bn}的前n项和
且S4=20,S8=340,b1=1,bn=3/4nSn,求Tn

答案

S8/S4=[a1(q^8-1)/(q-1)]/[a1(q^4-1)/(q-1)]=[a1(q^4+1)(q^4-1)/(q-1)]/[a1(q^4-1)/(q-1)]=q^4+1=340/20=17q^4=16q>0 q=2S4=a1(q^4-1)/(q-1)=a1(16-1)/(2-1)=15a1=20a1=4/3Sn=a1(q^n-1)/(q-1)=(4/3)(2^n-1)/(2-1)=(...