已知等差数列{an}的前n项和为Sn,且过点P(n,an)和Q(n+3,an+3)(n∈N*)的直线的斜率是4,若S1=3,则S6=______.-数学

题目简介

已知等差数列{an}的前n项和为Sn,且过点P(n,an)和Q(n+3,an+3)(n∈N*)的直线的斜率是4,若S1=3,则S6=______.-数学

题目详情

已知等差数列{an}的前n项和为Sn,且过点P(n,an)和Q(n+3,an+3)(n∈N*)的直线的斜率是4,若S1=3,则S6=______.
题型:填空题难度:偏易来源:台州二模

答案

由题意过点P(n,an)和Q(n+3,an+3)(n∈N*)的直线的斜率是4,
an+3-an
3
=4,即an+3-an=3d=12,d=4
又等差数列{an},S1=3,可得a1=3
所以S6=6a1+
n(n-1)
2
d=6×3+15×4=78
故答案为78

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