1:在等差数列中{an},a6/a4=7/11,且Sn是此数列前n项和,求S11/S7的和.2：已知两等差数列{an},{bn}前n项和之比为（4n+3):(2n+5),n是正自然数,求a8:b8.3：在等差数列{an}中,a1>0,3a8=5a13,若Sn为此数列前n项之和,则

Question

1:在等差数列中{an},a6/a4=7/11,且Sn是此数列前n项和,求S11/S7的和.
2：已知两等差数列{an},{bn}前n项和之比为（4n+3):(2n+5),n是正自然数,求a8:b8.
3：在等差数列{an}中,a1>0,3a8=5a13,若Sn为此数列前n项之和,则Sn中最大值是什么?n是正的自然数.

Answer 1

1、a6=a1+5d a4=a1+3d (a1+5d)/(a1+3d)=7/11
==> 11a1+55d=7a1+21d
S11=11a1+10*11/2*d=11a1+55d
S7 =7a1 +6*7/2*d =7a1 +21d
==> S11/S7=1
3、3(a1+7d)=5(a1+12d) ==> 2a1=-39d
Sn=n a1+ (n-1)n/2*d = 1/2*[2n a1+d*n^2-nd]
= 1/2*[n^2*d-40nd]
=d/2*[n^2-40n]
=d/2*[(n-20)^2-400]
=d/2*(n-20)^2 - 200d
a1>0 ==> d