Question

设等差数列{an}的前n项和为Sn 若S3=9 S5=20 则a7+a8+a9=？

Answer 1

S3=9
则A2 = S3/3 = 9/3 = 3

S5=20
则A3 = S5/5 = 20/5 = 4

推得公差D = A3-A2 = 4-3 = 1

A8 = A3 + 5D = 4 + 5 = 9

a7+a8+a9 = 3*A8 = 3*9 = 27

Answer 2

【a1＋a2＋a3】、【a4＋a5＋a6】、【a7＋a8＋a9】
M1 M2 M3
这三段的和也成等差数列，现在M1=9，M1＋M2=20，即：M2=11，则M3=13，所以
a7＋a8＋a9=13

追问

注意 是S5……

追答

S3=a1＋a2＋a3=3a2=9，则：a2=3
S5=a1＋a2＋a3＋a4＋a5=5a3=20，则：a3=4
则：an=n＋1
则：a7＋a8＋a9=8＋9＋10=27

追问

还是多谢了

Answer 3

S3=3a1+3d=9
S5=5a1+10d=20
所以a1=2，d=1
a7+a8+a9=3a8=3（a1+7d）=3*（2+7）=27