等差数列{an}中,若a1+a4=10,a2-a3=2,则此数列的前n项和Sn是(  ) A.n2+7n B.9n-n2 C.3n-n2 D.15n-n2

问题描述:

等差数列{an}中,若a1+a4=10,a2-a3=2,则此数列的前n项和Sn是(  )
A. n2+7n
B. 9n-n2
C. 3n-n2
D. 15n-n2

设等差数列{an}的首项为a1,公差为d,
∵a1+a4=10,a2-a3=2,∴d=-2,a1=8,
∴此数列的前n项和Sn=na1+

n(n−1)
2
d=9n-n2
故选B.