Futher-mathematics-topic-5.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,2017/2/21,#,Topic5.2,Generating the terms of a,first-order recurrence,relation,一,阶递推关系,A first-order recurrence relation relates a term in a sequence to the previous,term in,the same sequence,which means that we only need an initial value to be able,to generate,all remaining terms of a,sequence,一,阶递推关系是联系一个数列中的前一项和后一项，意味着我们只需要知道一个初始的值就可以求得数列里所有剩余的项,例子：,a,n,表示数列,第一,项 （首项）,a,1,第,n,项 记作,a,n,第,n+1,项，记作,a,n+1,a,n,=a,n-1,+3,表示第,n,项的值等于它的前一项的值再加上,3,；,简单的例子,sequence 1,5,9,13,17,u,n,+1=,u,n,+4,u,1,=1.,一阶递推关系表达了相邻两项的,例题,1,：,The following equations each define a sequence.Which of them are first-order,recurrence relations(defining a relationship between two consecutive terms)?,a,un,=,un,1,+,2,u,1,=,3,n,=,1,2,3,b,un,=,4,+,2,n n,=,1,2,3,c,fn,+,1,=,3,fn n,=,1,2,3,