An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which each term is obtained by adding a constant value to the previous term. The constant value is called the common difference, and it determines the pattern of the sequence.
The formula for finding the nth term in an arithmetic progression is: an = a1 + (n-1)d, where an represents the nth term, a1 represents the first term, and d represents the common difference.
To determine if a sequence is an arithmetic progression, you can check if the difference between consecutive terms is constant. If the difference is the same for every pair of terms, then the sequence is an arithmetic progression.
Yes, an arithmetic progression can have a negative common difference. This means that the sequence is decreasing instead of increasing. For example, an arithmetic progression with a first term of 10 and a common difference of -3 would be: 10, 7, 4, 1, -2, ...
Arithmetic progressions are commonly used in finance and economics to model linear growth or depreciation. They are also used in physics to describe the motion of an object with a constant acceleration. In computer science, arithmetic progressions are used in algorithms and data structures to perform sequential operations on a set of data.