geometric progression

简明释义

几何级数

英英释义

例句

1.In finance, compound interest can be understood as a geometric progression 几何级数 where the principal amount increases exponentially.

在金融中，复利可以理解为一种几何级数，本金呈指数增长。

2.The sequence of payments in an annuity can often form a geometric progression 几何级数 depending on the interest rate.

年金中的支付序列通常可以形成几何级数，这取决于利率。

3.The lengths of the sides of similar triangles are in a geometric progression 几何级数 based on their scale factor.

相似三角形的边长根据它们的比例因子呈现几何级数。

4.The population of the bacteria grew in a geometric progression 几何级数 over a week, doubling every 24 hours.

细菌的数量在一周内以几何级数增长，每24小时翻倍。

5.When modeling the spread of a rumor, we can assume it follows a geometric progression 几何级数 as more people hear it.

在建模谣言传播时，我们可以假设它遵循几何级数，因为越来越多的人听说。

作文

In mathematics, a geometric 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 concept is not only fundamental in mathematics but also has significant applications in various fields such as finance, physics, and computer science. Understanding geometric progression can help us analyze growth patterns, calculate interest rates, and even model certain natural phenomena.For instance, consider the scenario of compound interest in finance. When money is invested in a savings account, the interest earned is often compounded, meaning that each period's interest is calculated based on the total amount in the account, including previous interest. This results in a geometric progression of the account balance over time. If you invest $100 at an interest rate of 5% per year, the balance after one year would be $105. The following year, the interest is calculated on $105, leading to a balance of $110.25. This pattern continues, illustrating how investments grow exponentially—an essential principle for anyone looking to understand personal finance and investment strategies.Moreover, geometric progression appears frequently in nature. For example, population growth can often be modeled using this mathematical concept. If a certain species reproduces at a consistent rate, the population can double at regular intervals, leading to a rapid increase that follows a geometric progression. This exponential growth can have profound implications for ecosystems and biodiversity, making it critical for ecologists and conservationists to understand.In computer science, algorithms with logarithmic time complexity often exhibit characteristics of geometric progression. For instance, binary search algorithms halve the data set with each iteration, which can be seen as a geometric progression in terms of the number of elements being processed. This efficiency is crucial for developing fast and effective algorithms, especially when dealing with large data sets.Understanding geometric progression is not limited to academic pursuits; it also enhances our everyday decision-making. Whether we are planning a budget, analyzing trends, or predicting future outcomes, recognizing patterns that follow a geometric progression can provide valuable insights. It encourages a deeper appreciation of how various factors interact over time and allows us to make more informed choices.In conclusion, the concept of geometric progression is a powerful tool that extends beyond theoretical mathematics. Its applications in finance, biology, computer science, and daily life illustrate its importance. By mastering this concept, individuals can better navigate the complexities of growth and change in a variety of contexts. As we continue to encounter situations where geometric progression plays a role, we gain not only mathematical knowledge but also practical skills that enhance our understanding of the world around us.

在数学中，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字（称为公比）来找到的。这个概念不仅在数学中是基础性的，而且在金融、物理和计算机科学等多个领域也具有重要的应用。理解几何级数可以帮助我们分析增长模式、计算利率，甚至建模某些自然现象。例如，考虑金融中的复利场景。当钱存入储蓄账户时，获得的利息通常是复利的，这意味着每个时期的利息是基于账户中的总金额计算的，包括之前的利息。这导致了账户余额随时间呈现出几何级数的模式。如果你以5%的年利率投资100美元，那么一年后的余额将是105美元。第二年，利息是基于105美元计算的，导致余额为110.25美元。这个模式不断重复，说明投资是如何呈指数增长的——这是任何希望理解个人财务和投资策略的人都必须掌握的基本原则。此外，几何级数在自然界中经常出现。例如，人口增长通常可以用这个数学概念建模。如果某种物种以一致的速度繁殖，人口就会在规律的时间间隔内翻倍，导致快速增长，遵循几何级数。这种指数增长对生态系统和生物多样性有深远的影响，因此对于生态学家和保护主义者来说，理解这一点至关重要。在计算机科学中，具有对数时间复杂度的算法通常表现出几何级数的特征。例如，二分搜索算法在每次迭代中将数据集减半，这可以看作是处理的元素数量呈现出几何级数。这种效率对于开发快速有效的算法至关重要，尤其是在处理大数据集时。理解几何级数不仅限于学术追求；它还增强了我们日常决策的能力。无论是制定预算、分析趋势还是预测未来结果，识别遵循几何级数的模式都可以提供有价值的见解。它鼓励我们更深入地认识各种因素如何随时间相互作用，并使我们能够做出更明智的选择。总之，几何级数的概念是一个强大的工具，超越了理论数学。它在金融、生物学、计算机科学和日常生活中的应用展示了它的重要性。通过掌握这个概念，个人可以更好地驾驭各种背景下的增长和变化的复杂性。随着我们继续遇到几何级数发挥作用的情况，我们不仅获得了数学知识，还获得了增强我们对周围世界理解的实用技能。