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
问题描述：
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
答
-1/3 + (-2/3) + (-4/3)+.....=-1/3*(1-2的n次方)/(1-2)=(1-2的n次方)/3
答
∵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-7/3sn=(a1+an)n/2=(-1/3+2n-7/3)n/2=(2n-8/3)n/2=(n-4/3)n...