设数列{}是等差数列,数列{}是等比数列,记数列{},{}的前n项和分别为Sn,Tn．若a5＝b5,a6＝b6,设数列{an}是等差数列,数列{bn}是等比数列,记数列{an},{bn}的前n项和分别为Sn,Tn．若a5＝b5,a6＝b6,

Question

设数列{ }是等差数列,数列{ }是等比数列,记数列 { },{ }的前n项和分别为 Sn,Tn ．若a5＝b5,a6＝b6,
设数列{an }是等差数列,数列{ bn}是等比数列,记数列
{an },{ bn}的前n项和分别为 Sn,Tn ．若a5＝b5,a6＝b6,
且S7－S5＝4（T6－T4）,则(a7+a5)/(b7+b5) ＝____________.

Answer 1

答案是-5/13
由S7－S5＝4（T6－T4）可得a7+a6=4（b6+b5）=4（a6+a5）,就可以得到首项公差的关系：a1＝-25d/6
由a5＝b5,a6＝b6得a5/a6=b5/b6=1/q,将a1＝-25d/6
代入上面的关系式就可以求得等比数列的公比q=-5
(a7+a5)/(b7+b5) =2a6/(b7+b5)=2b6/(b7+b5)=2q/1+q^2=-10/26=-5/13