arithmetic progression

简明释义

算术级数

英英释义

例句

1.The monthly payments of a loan can be modeled as an arithmetic progression 等差数列 if they increase by a fixed amount each month.

如果贷款的每月还款额每月增加固定金额，则可以将其建模为arithmetic progression 等差数列。

2.To find the sum of the first n terms of an arithmetic progression 等差数列, you can use the formula S = n/2 * (a + l).

要找出前n项的和，可以使用公式S = n/2 * (a + l)来计算arithmetic progression 等差数列的和。

3.An arithmetic progression 等差数列 can be used to predict future values in a linear growth scenario.

在线性增长场景中，可以使用arithmetic progression 等差数列来预测未来值。

4.In an arithmetic progression 等差数列, the difference between consecutive terms is constant.

在arithmetic progression 等差数列中，相邻项之间的差是恒定的。

5.The sequence of numbers 2, 4, 6, 8 is an example of an arithmetic progression 等差数列.

数字序列2, 4, 6, 8是一个例子，属于arithmetic progression 等差数列。

作文

Arithmetic progression, often abbreviated as AP, is a fundamental concept in mathematics that refers to a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the 'common difference.' For example, in the sequence 2, 5, 8, 11, 14, each term increases by 3, illustrating an arithmetic progression (等差数列). Understanding arithmetic progression is essential not only in pure mathematics but also in various real-world applications, such as finance, computer science, and even art.One of the most interesting aspects of arithmetic progression is its simplicity and the ease with which it can be applied. The formula for the nth term of an arithmetic progression is given by: a_n = a + (n - 1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number. This formula allows us to quickly calculate any term in the sequence without having to list all previous terms.In practical situations, we often encounter arithmetic progression in financial contexts. For instance, if you invest a fixed amount of money every month into a savings account, the total amount saved forms an arithmetic progression. Each month, the amount saved increases by a constant value, which can help individuals understand their savings growth over time.Moreover, arithmetic progression can also be observed in daily life. Consider a scenario where a person runs a certain distance each day, increasing the distance by a fixed amount daily. If they start by running 1 kilometer on the first day and increase their distance by 0.5 kilometers each subsequent day, their running distances form an arithmetic progression of 1, 1.5, 2, 2.5, and so on. This pattern helps in planning training schedules and achieving fitness goals.In addition to practical applications, arithmetic progression has significant implications in theoretical mathematics. It serves as a foundation for more complex mathematical concepts, such as sequences and series. For example, the sum of the first n terms of an arithmetic progression can be calculated using the formula S_n = n/2 * (a + l), where 'S_n' is the sum of the first n terms, 'a' is the first term, and 'l' is the last term. This formula is particularly useful in solving problems related to series and can be used to derive other important mathematical results.In conclusion, the concept of arithmetic progression (等差数列) is not just a theoretical construct; it is a practical tool that can be applied in various aspects of life. Whether it's managing finances, planning workouts, or diving deeper into mathematical studies, understanding arithmetic progression equips individuals with valuable skills. By recognizing patterns and applying the formulas associated with arithmetic progression, one can enhance problem-solving abilities and make informed decisions in everyday life.

等差数列，通常缩写为AP，是数学中的一个基本概念，指的是一系列数字的序列，其中连续项之间的差是恒定的。这个恒定的差称为“公差”。例如，在序列2、5、8、11、14中，每个项增加3，说明了一个等差数列。理解等差数列不仅在纯数学中至关重要，而且在金融、计算机科学甚至艺术等各种现实应用中也同样重要。等差数列最有趣的方面之一是它的简单性及其应用的便利性。等差数列的第n项公式为：a_n = a + (n - 1)d，其中'a'是首项，'d'是公差，'n'是项数。这个公式使我们能够快速计算序列中的任何项，而不必列出所有先前的项。在实际情况下，我们经常在金融上下文中遇到等差数列。例如，如果你每月固定存入一笔钱到储蓄账户中，那么总存款形成了一个等差数列。每个月，存入的金额以恒定的值增加，这可以帮助个人了解他们的储蓄增长情况。此外，等差数列也可以在日常生活中观察到。考虑一个场景，一个人每天跑一定的距离，并且每天增加固定的距离。如果他们第一天跑1公里，并且之后每天增加0.5公里，他们的跑步距离形成了1、1.5、2、2.5等的等差数列。这种模式有助于制定训练计划并实现健身目标。除了实际应用，等差数列在理论数学中也具有重要意义。它为更复杂的数学概念，如序列和级数奠定了基础。例如，前n项的和可以使用公式S_n = n/2 * (a + l)进行计算，其中'S_n'是前n项的和，'a'是首项，'l'是末项。这个公式在解决与级数相关的问题时尤其有用，并且可以用来推导其他重要的数学结果。总之，等差数列（等差数列）这一概念不仅仅是一个理论构造；它是一个可以应用于生活各个方面的实用工具。无论是管理财务、制定锻炼计划，还是深入研究数学，理解等差数列都能为个人提供宝贵的技能。通过识别模式并应用与等差数列相关的公式，人们可以增强解决问题的能力，并在日常生活中做出明智的决定。