Question

等差数列{an}的前n项和为Sn,且6S5-5S3=5,则a4=

等差数列{an}的前n项和为Sn,且6S5-5S3=5,则a4=

Answer 1

解：
6S5－5S3＝5
由等差数列前n项和公式Sn＝na1＋[n(n－1)/2]*d，得：
S5＝5a1＋[(5×4)/2]*d＝5a1＋10d
S3＝3a1＋[(3×2)/2]*d＝3a1＋3d
∴6(5a1＋10d)－5(3a1＋3d)＝5
即15a1＋45d＝5
故a1＋3d＝1/3
即a4＝1/3.

Answer 2

6S5-5S3=5;
30a3 - 15a2 = 5;
2a3-a2=1/2;
2a3 = a2+a4;
所以，a4 = 1/2