等差数列{an}中,an-4=30,且前9项的和S9=18,前n项和为Sn=240,则n等于(  ) A.15 B.16 C.17 D.18

问题描述:

等差数列{an}中,an-4=30,且前9项的和S9=18,前n项和为Sn=240,则n等于(  )
A. 15
B. 16
C. 17
D. 18

根据等差数列的性质得S9=a1+a2+…+a9=9a5=18,
所以a5=2,且a1+an=a5+an-4
则Sn=

n(a1+an
2
=
n(a5+an−4
2
=
n(2+30)
2
=240,
即16n=240,解得n=15
故选A.