Question

以Sn,Tn分别表示等差数列{an},{bn}的前n项和,若Sn/Tn=n/(n+3),则a4/b5的值为

Answer 1

设等差数列an的首项和公差分别为a,d1

设等差数列bn的首项和公比分别为b,d2

Sn = (2a + (n-1)d1) n / 2

Tn = (2b + (n-1)d2) n / 2

Sn / Tn = n / (n + 3) => d1 = d2,d1 = 2a ,b = 4a

所以 a4 / b5 = (a + 3d1) / (b + 4d2) = (a +6a) / (4a + 8a) = 7 / 12