已知等差数列{an}的前n次和为sn,且S2=10,S5=55,则过点P(n,an)和Q(n+2,an+2)(n∈-N*)的直线方向向量的坐标可以是_.

问题描述:

已知等差数列{an}的前n次和为sn,且S2=10,S5=55,则过点P(n,an)和Q(n+2,an+2)(n∈-N*)的直线方向向量的坐标可以是______.

∵等差数列{an}的前n项和为Sn,且S2=10,S5=55,∴a1+a2=10,a3=11,∴a1=3,d=4,∴an=4n-1an+2=4n+7,∴P(n,4n-1),Q(n+2,4n+7)∴直线PQ的斜率是 4n+7−4n+1n+2−n=4,∴过点P(n,an)和Q(n+2,an+2)(n...