等差数列{an}，{bn}的前n项和分别为An，Bn，且AnBn＝7n+45n+3，则a5b5=．

Question

等差数列{a_n}，{b_n}的前n项和分别为A_n，B_n，且(An)/(Bn)＝(7n+45)/(n+3)，则(a5)/(b5)=______．

Answer 1

∵数列{a_n}，{b_n}均为等差数列，且其前n项和分别为A_n，B_n，
∴(a5)/(b5)＝((a1+a9)/(2))/((b1+b9)/(2))=(((a1+a9)•9)/(2))/(((b1+b9)•9)/(2))＝(A9)/(B9)．
∵(An)/(Bn)＝(7n+45)/(n+3)，
∴(a5)/(b5)＝(A9)/(B9)＝(7×9+45)/(9+3)＝9．
故答案为：9．