Sixth Term of an Arithmetic Sequence
What is the sixth term of the arithmetic sequence if the first term is 3 and the common difference is 2?
An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant, called the common difference. This problem involves finding a specific term within such a sequence, given the first term and the common difference. In general, the nth term of an arithmetic sequence can be calculated using the formula: nth term = first term + (n-1) * common difference. By understanding this formula, you gain the ability to dissect any arithmetic sequence problem, especially when needing to find a specific term number. The problem showcases the simplicity of arithmetic sequences and offers a straightforward calculation approach that reinforces the concept of linear growth. This understanding is fundamental in introductory algebra and serves as a basis for more complex topics such as geometric sequences or exploring sequences in the context of calculus. Sequences offer a way to understand progressive changes and are foundational in mathematical analysis. Such problems help strengthen one's ability to recognize patterns, which is a critical skill in higher-level math courses and real-world applications.