问题 选择题
已知数列{an}满足an+1+an-1=2an,n>2,点O是平面上不在L上的任意一点,L上有不重合的三点A、B、C,又知a2
OA
+a2009
OC
=
OB
,则S2010=(  )
A.1004B.2010C.2009D.1005
答案

∵A、B、C三点共线,

AB
AC

OB
-
OA
=λ(
OC
-
OA
),

OB
=(1-λ)
OA
OC

a2

OA
+a2009
OC
=
OB

∴a2+a2009=1,

∵an+1+an-1=2an,n>2,

∴{an}为等差数列,

∴s2010=

a1+a2010
2
×2010

=

a2+a2009
2
×2010

=1005.

故选D.

判断题
单项选择题 配伍题