progresija

Progresija is a term used in mathematics to describe a sequence of numbers where each term is related to the previous one by a consistent rule. This rule typically involves either adding a fixed difference or multiplying by a fixed ratio.

The most common types of progresija are arithmetic progression and geometric progression. In an arithmetic progression, the difference between consecutive terms is constant. For example, the sequence 2, 4, 6, 8, 10 is an arithmetic progression with a common difference of 2. In a geometric progression, the ratio between consecutive terms is constant. For instance, the sequence 3, 6, 12, 24, 48 is a geometric progression with a common ratio of 2.

The concept of progresija is fundamental in various areas of mathematics, including algebra, calculus, and number theory. It is used to model phenomena that exhibit a steady growth or decay, such as compound interest in finance or population growth. Understanding the properties of different types of progresija allows for predictions and calculations involving sequences. Formulas exist to determine the nth term of an arithmetic or geometric progression and to calculate the sum of a finite number of terms. These formulas are derived from the consistent nature of the progression's defining rule. Beyond these basic forms, more complex progressions can be defined with intricate relationships between their terms.