arithmetic sequence
发音：/??r?θ??m?t?k s??e?z??/
英语范文：
In mathematics, an arithmetic sequence is a sequence of numbers that repeats itself with a regular pattern. It is formed by adding a constant value to each term of the sequence, resulting in a series of numbers that gradually increase or decrease in a predictable way.
For example, consider the sequence 1, 3, 5, 7, 9. Each term is the sum of the previous term plus 2, resulting in an arithmetic sequence.
The properties of an arithmetic sequence include the fact that the sum of any consecutive terms is equal to the average of those terms, and that the largest term will always be greater than or equal to the smallest term.
Applications of arithmetic sequences are widespread, as they can be used to model many real-world phenomena, such as population growth, temperature fluctuations, or the sequence of numbers in a musical scale.
In summary, an arithmetic sequence is a mathematical concept that can be used to describe patterns in numerical sequences and is fundamental in many areas of mathematics and beyond.
音标和基础释义：
在数学中，算术序列是一种以规律模式重复的数字序列。它是由一个常数值加到序列中的每个项形成的，形成了一个逐渐增加或减少的可预测的数字系列。
例如，考虑序列中的数字1，3，5，7，9。每个项都是前一项加上2的结果，形成了一个算术序列。
算术序列的性质包括任何连续项的总和等于这些项的平均值，以及最大的项总是大于或等于最小的项。
算术序列的应用非常广泛，因为它可以用来模拟许多现实世界的现象，如人口增长、温度波动或音乐音阶中的数字序列。
总的来说，算术序列是一种数学概念，可用于描述数字序列的模式，在数学和其他领域的许多方面都是基础性的。
Arithmetic Sequence
Arithmetic sequence是一种非常常见的数列形式，它的特点是每一项都按照一定的规律逐渐增加或减少。这种数列在现实生活中有着广泛的应用，例如在建筑工程、金融、生物科学等领域。
基础释义
一个等差数列的每一项按照一定的公差d逐渐增加或减少，其通项公式为an=a1+（n-1）d。其中，a1是数列的第一项，an是数列的第n项。
发音：'?r?θ?mt?s?s?s'
英语范文
在我看来，arithmetic sequence在我们的日常生活中起着至关重要的作用。例如，当我们学习数学、物理或其他需要计算和推理的学科时，我们经常使用arithmetic sequence来解决问题。此外，在建筑工程中，工程师们经常使用arithmetic sequence来计算和预测建筑物的重量和稳定性。
此外，arithmetic sequence在金融领域也有着广泛的应用。例如，贷款机构经常使用arithmetic sequence来计算利率和还款期限，以确保公平和透明。同时，生物学家也发现arithmetic sequence在物种进化、遗传学和生物钟等方面有着重要的作用。
总的来说，arithmetic sequence是一种非常有用的数学工具，它可以帮助我们更好地理解和解决各种问题。我们应该更加重视和利用这种数学工具，以更好地服务于我们的生活和工作。
Arithmetic sequence
Arithmetic sequence is a mathematical concept that refers to a sequence of numbers that increase or decrease in a regular pattern. It is a fundamental concept in mathematical analysis and other areas of mathematics.
In an arithmetic sequence, each term is equal to the previous term plus a constant difference, called the common difference. This difference is constant for all terms in the sequence.
For example, consider the sequence of numbers 5, 8, 11, 14. In this sequence, the first term is 5, the second term is 8, the third term is 11, and so on. It can be seen that each term increases by a constant amount of 3 from the previous term. Therefore, this sequence is an arithmetic sequence.
Arithmetic sequences are very useful in many practical applications, such as calculating averages and finding patterns in data. They are also used in various mathematical problems and algorithms.
In summary, an arithmetic sequence is a sequence of numbers that increase or decrease in a regular pattern and have a constant difference between each term. Understanding arithmetic sequences and their properties is essential for effective mathematical analysis and problem-solving.
[英语范文]
Arithmetic Sequence in Life
Life is full of arithmetic sequences. We can see them everywhere, from our daily routines to major life events.
For example, consider the sequence of steps we take to reach our destination. Each step is equal to the previous step plus the height of the step. This is an arithmetic sequence, with a constant difference between each step.
Similarly, we can see arithmetic sequences in our work and studies. For instance, if we have a task list with tasks of different levels of difficulty, then each task will be completed at a certain time interval based on its difficulty level. This is another example of an arithmetic sequence.
Arithmetic sequences are also used in various mathematical models to describe real-world phenomena. For instance, the growth rate of a company or population can be described by an arithmetic sequence, which helps us understand patterns and trends in these systems.
In conclusion, arithmetic sequences are fundamental concepts that are used widely in various contexts, from mathematics to real-world applications. Understanding these sequences and their properties is essential for effective problem-solving and decision-making.
