geometrical progression

简明释义

几何级数

英英释义

例句

1.The growth of the investment followed a geometrical progression due to reinvested earnings.

由于再投资收益，投资的增长遵循了几何级数。

2.The number of views on the video went up in a geometrical progression after it was shared on social media.

视频的观看次数在社交媒体分享后以几何级数上升。

3.The population of the bacteria increased in a geometrical progression over the course of a week.

细菌的数量在一周内以几何级数增长。

4.The series of payments was structured in a geometrical progression to ensure increasing returns.

付款系列被结构化为几何级数，以确保回报递增。

5.In finance, compound interest can be calculated using a geometrical progression formula.

在金融中，复利可以使用几何级数公式进行计算。

作文

In mathematics, the concept of geometrical progression is fundamental and widely applicable across various fields. A geometrical progression is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This characteristic makes geometrical progression distinct from arithmetic progression, where each term is obtained by adding a constant value to the previous term. Understanding geometrical progression is essential for students and professionals alike, as it has practical applications in finance, computer science, and natural sciences.One of the most common examples of a geometrical progression is the growth of populations. If a certain species of bacteria doubles in size every hour, the population can be represented as a geometrical progression. Starting with one bacterium, after one hour there are two, after two hours there are four, after three hours there are eight, and so on. The formula for the nth term of a geometrical progression is given by a_n = a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number. In our example, the first term 'a' is 1, and the common ratio 'r' is 2.Another practical application of geometrical progression is in finance, particularly in calculating compound interest. When money is invested at a certain interest rate compounded annually, the amount of money grows in a geometrical progression. For instance, if you invest $1000 at an annual interest rate of 5%, the amount after one year would be $1050, after two years it would be $1102.50, and after three years it would be approximately $1157.63. Each of these amounts can be seen as terms in a geometrical progression, where the common ratio reflects the growth factor of the investment.Moreover, geometrical progression also appears in the field of computer science, particularly in algorithms that have exponential time complexity. For example, certain recursive algorithms may exhibit behavior where the number of operations required grows in a geometrical progression. Understanding this growth pattern helps programmers optimize their code and make informed decisions about algorithm selection.In conclusion, the concept of geometrical progression is not only a mathematical curiosity but also a powerful tool that finds relevance in real-world applications. Its ability to model growth processes in biology, finance, and computer science makes it an essential topic for anyone looking to deepen their understanding of mathematics. By grasping the principles behind geometrical progression, individuals can apply these concepts to analyze and solve problems in various domains effectively. Thus, the study of geometrical progression is crucial for both academic pursuits and practical applications in everyday life.

在数学中，几何级数的概念是基本的，并且广泛适用于各个领域。几何级数是一个数字序列，其中每个项都是通过将前一个项乘以一个固定的非零数（称为公比）来找到的。这一特性使得几何级数与算术级数不同，后者是通过将一个常数值加到前一个项上来获得每个项。理解几何级数对学生和专业人士来说至关重要，因为它在金融、计算机科学和自然科学中具有实际应用。几何级数最常见的一个例子是种群的增长。如果某种细菌每小时翻倍，其种群可以表示为几何级数。从一个细菌开始，经过一个小时后有两个，经过两个小时后有四个，经过三个小时后有八个，依此类推。几何级数第n项的公式为a_n = a * r^(n-1)，其中'a'是第一项，'r'是公比，'n'是项数。在我们的例子中，第一项'a'是1，公比'r'是2。几何级数的另一个实际应用是在金融领域，特别是在计算复利时。当钱以某个年利率投资时，金额以几何级数增长。例如，如果您以5%的年利率投资1000美元，那么一年后的金额将是1050美元，两年后将是1102.50美元，三年后将约为1157.63美元。每一个金额都可以看作是几何级数中的项，其中公比反映了投资的增长因子。此外，几何级数还出现在计算机科学领域，特别是在具有指数时间复杂度的算法中。例如，某些递归算法可能表现出所需操作数量以几何级数增长的行为。理解这种增长模式可以帮助程序员优化代码并做出明智的算法选择。总之，几何级数的概念不仅仅是一个数学好奇心，而是一个强大的工具，在现实世界的应用中找到了相关性。它能够模拟生物学、金融和计算机科学中的增长过程，使其成为任何希望加深数学理解的人的重要主题。通过掌握几何级数背后的原理，个人可以有效地将这些概念应用于分析和解决各种领域的问题。因此，学习几何级数对学术追求和日常生活中的实际应用都是至关重要的。