There are 2008 numbers placed in the line as 0,1,3,8,21 disregarding the 1st and the end,evey term

题目

There are 2008 numbers placed in the line as 0,1,3,8,21 disregarding the 1st and the end,evey term
thereafter if multiplied by 3,the answer will aways be the sum of the number on its left and the number on its right .what is the remainder when the rightmost is divided

答案

题目是这样的：有2008个数这样排练着:0,1,3,8,21.忽略第一个和最后一个数,（剩下的）每个数乘以3都等于这个数左边与右边的两个数的和,那么最右边那个数除以3的余数是多少?
根据题中所给的规律,可知z这个数列符合3Cn=Cn-1+Cn+1 (n>1),
因此推算出21后的几项后为0,1,3,8,21,55,144,377,987.
忽略第一个数0,看剩下的数除以3后的余数,依次为1,0,2,0,1,0,2,0.
归纳推理可得其余数的规律就是每四项重复1,0,2,0
最右边的数是第2008项,但是由于我们忽略了第一个数0,所以应该用2007除以4得到余数为3
因此 按照已找出的余数的规律,知道其结果为2
希望我的回答能帮到你