设数列{an}满足a1=-1/3,且对任意的n属于N+,点Pn(n,an)都满足向量PnPn+1=(1,2)求数an的列前n项和Sn

Question

设数列{an}满足a1=-1/3,且对任意的n属于N+,点Pn(n,an)都满足向量PnPn+1=(1,2)求数an的列前n项和Sn

Answer 1

∵Pn(n.an)
∴P(n+1)=(n+1.an+1)
又∵向量PnP(n+1)=(1,2),
∴（an+1）-an=2
∴是首项为-1/3,公差为2的等差数列
∴an=a1+2(n-1)
=-1/3+2n-2
=2n-7/3
sn=(a1+an)n/2
=(-1/3+2n-7/3)n/2
=(2n-8/3)n/2
=(n-4/3)n