Question

已知an是等差数列，Sn是前n项和，且a2＝3a4－6，则S9等于多少？怎么解啊？要过程，谢谢了！说详细点儿！

Answer 1

an是等差数列,所以a4 -a2=2(a5 -a4)
a5=(3a4-a2)/2=3
S9=9a5=9*3=27

Answer 2

a4=a2+2d
a2＝3a4－6

a2=3(a2+2d)-6
2a2=6-6d
a2=3-3d
a1=a2-d=3-4d

an=a1+(n-1)d=3+(n-5)d
Sn=(a1+an)n/2=6n+(n-9)n*d/2
S9=6*9-(9-9)*9*d/2=27

Answer 3

a2＝3a4－6
3a4-a2=6
3a1+9d-a1-d=6
2（a1+4d）=6
a5=3
S9=9a5=27

Answer 4

a2=3a4-6即a2=3(a2+2d)-6 其中d是公差
所以a2=3-3d得a5=a2+3d=3-3d+3d=3
s9=a1+a2+a3+````+a7+a8+a9=(a1+a9)+(a2+a8)+(a3+a7)+(a4+a6)+a5=9a5=9*3=27