20th Term of Arithmetic Sequence Formula
Write a formula to find the 20th term of the arithmetic sequence where the first term is 3 and the common difference is 2.
In this problem, we are dealing with an arithmetic sequence, a fundamental concept in the study of sequences and series. An arithmetic sequence is one in which each term after the first is obtained by adding a constant difference to the previous term. In this particular problem, you are asked to find the 20th term given the first term and the common difference. This requires recognizing the pattern inherent in arithmetic sequences and applying the formula for the n-th term of an arithmetic sequence. The formula is generally written as the first term plus the product of the term number minus one times the common difference. Understanding how to manipulate this formula is crucial for solving problems related to sequences and provides the foundation for more complex series analysis.
When working with arithmetic sequences, it's important to consider their properties, such as how the common difference impacts the growth of the sequence and its linear characteristics. This sequence demonstrates a straightforward progression, allowing you to explore how changes in the common difference and the position of the term in the sequence affect the result. Comprehending these dynamics is essential for delving into more advanced topics within the field of sequences and series.