{an}是等差数列,公差为1 a1+a2+\\+a99=99,a3+a6+a9+\\+a99=

题目

{an}是等差数列,公差为1 a1+a2+\\+a99=99,a3+a6+a9+\\+a99=

答案

等差数列的通项公式是
an=a1+(n-1)d a1+a2+...+a99
=a1+a1+d+a1+2d+...+a1+98d
=99a1+d+2d+...+98d
=99a1+98(98+1)/2d
=99a1+4851=99 a1
=(99-4851)/99=-48
a3+a6+a9+...+a99
=33a1+2d+5d+8d+...+98d
=-33*48+1650 =66