>
数学
>
已知等差数列{a
n
}中,a
n
≠0,且 a
n-1
-a
n
2
+a
n+1
=0,前(2n-1)项和S
2n-1
=38,则n等于( )
A. 10
B. 19
C. 20
D. 38
人气:229 ℃ 时间:2020-02-01 07:12:51
解答
∵数列{a
n
}为等差数列,
∴2a
n
=a
n-1
+a
n+1
,又a
n-1
-a
n
2
+a
n+1
=0,
∴a
n
(2-a
n
)=0,
∵a
n
≠0,∴a
n
=2,
又S
2n-1
=
(2n−1)(
a
1
+
a
2n−1
)
2
=(2n-1)a
n
=2(2n-1)=38,
∴2n-1=19,
则n=10.
故选A
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