QQ登录
微博登录 
雅思阅读
2016-08-26 14:27
来源：新东方整理
作者：上海新东方
Revision: Sequences
Introduction
In the sequence 2, 4, 6, 8, 10.., there is an obvious pattern. Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replaces the n's by 4's: 4th term 2 × 4 = 8.
Example
What is the nth term of the sequence 2, 5, 10, 17, 26... ? The easiest way to find the nth term is by trial and error.
n | 1 - 2 - 3 - 4 - 5
n² | 1 - 4 - 9 - 16 - 25
n² + 1 | 2 - 5 - 10 - 17 - 26
This is the required sequence, so the nth term is n² + 1. For some sequences, there is no easy way of working out the nth term of a sequence, other than to try different possibilities.
Tips: if the sequence is going up in threes (e.g. 3, 6, 9, 12...), there will probably be a three in the formula, etc.
In many cases, square numbers will come up, so try squaring n, as above. Also, the triangular numbers formula often comes up.
Notation
The nth term of a sequence is usually written as Un. So in the last example, Un = n² + 1. The 5th term is therefore U5 = 25 + 1=26.
Recurrence relation
This is where the next term of a sequence is defined using the previous term(s). For example, the recurrence relation for 2, 4, 8, 16, 32, ... would be: U1 = 2, Un = 2(Un-1). This tells us that the first term, U1, is 2 and the next term of the sequence can be found by doubling the previous term.
Convergent Sequences
Sequences whose nth term approaches a finite number as n becomes larger are known as convergent sequences and the number to which the sequence converges are known as the limit of the sequence. For example: 10, 5, 2.5, 1.25, 0.625, ... converges towards the limit zero.
推荐阅读
若想获取更多详尽出国留学攻略以及雅思备考资讯，可以打开我们【上海新东方雅思网】，涵盖雅思真题机经，雅思写作、口语、听力、阅读以及留学名校介绍等，也许就能找到你真正需要的。上海新东方雅思网在这里预祝各位考生学习顺利，都能考取自己满意的学校。
|
上海新东方寒假班报名地址
|
||||
|
|
||||
扫码添加大队长Sam，领取最新沪上热门国际学校招生信息
A BETTER YOU,A BIGGER WORLD!
版权及免责声明
①凡本网注明"稿件来源：新东方"的所有文字、图片和音视频稿件，版权均属新东方教育科技集团（含本网和新东方网） 所有，任何媒体、网站或个人未经本网协议授权不得转载、链接、转贴或以其他任何方式复制、发表。已经本网协议授权的媒体、网站，在下载使用时必须注明"稿件来源：新东方"，违者本网将依法追究法律责任。
② 本网未注明"稿件来源：新东方"的文/图等稿件均为转载稿，本网转载仅基于传递更多信息之目的，并不意味着赞同转载稿的观点或证实其内容的真实性。如其他媒体、网站或个人从本网下载使用，必须保留本网注明的"稿件来源"，并自负版权等法律责任。如擅自篡改为"稿件来源：新东方"，本网将依法追究法律责任。
③ 如本网转载稿涉及版权等问题，请作者见稿后在两周内速来电与新东方网联系，电话：010-60908555。
雅思阅读
