等差数列

The essay discusses the characters of the second order linear recurrent sequence, which any number three , number four and number five terms of sequence nestie up, and develops the definition of the arithmetical progress and the geometric series in the united form according to these characters.

讨论了二阶线性递归数列任意相邻三项、四项、五项的性质，并且由性质导出了等差数列与等比数列在统一形式意义下的定义。

In this paper the different methods ti find general term formulas of power series sum functions,by means of which coefficients are higher arithmetical of geometrical sequence .

利用差分法导出了求幂级数和函数的一个通项公式，用它能求出系数为高阶等差数列和高阶等比数列的幂级数∑∞n=0 anxn的和函数

The same for Aristotle, with most of his biological taxonomical theories lived even over 2000 years, some of them were not challenged until 150 years ago.

古埃及人已经能解决一些属于一次方程和最简单的二次方程的问题，还有一些关于等差数列、等比数列的初步知识。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。