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
答
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
=240,n(2+30) 2
即16n=240,解得n=15
故选A.