>
数学
>
已知数列{a
n
}满足
a
1
=0,
a
n+1
=
a
n
+1+2
a
n
+1
(n∈
N
*
)
,则a
99
=( )
A. 10001
B. 9999
C. 9900
D. 9800
人气:368 ℃ 时间:2019-09-29 03:14:46
解答
两边同加1得
a
n+1
+1 =
a
n
+1+2
a
n
+1
+1
∴
a
n+1
+1
=
a
n
+1
+1
∴
数列{
a
n
+1
}
是以1为首项,1为公差的等差数列
∴
a
n
+1
=n
∴a
n
=n
2
-1
当n=99时,a
99
=9800
故选D.
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