How to Find the 15th Term of an Arithmetic Sequence: A Comprehensive Guide

Introduction to Arithmetic Sequences

Arithmetic sequences, often referred to as arithmetic progressions, are sequences of numbers where each term after the first increases by a constant difference, known as the common difference. This article will guide you through finding the 15th term of a specific arithmetic sequence, namely 14, 18, 22, 26, and 30. We'll cover the formula to find the nth term, the value of the 15th term, and a detailed explanation of the process.

Understanding the Arithmetic Sequence and Its Components

Consider the arithmetic sequence: 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70. This sequence follows a pattern where each term increases by 4. Here, the first term (a1) is 14, and the common difference (d) is 4.

The general formula for finding the nth term (an) of an arithmetic sequence is given by:

Formula: an a1 (n - 1) x d

Here, a1 represents the first term, d is the common difference, and n is the term position in the sequence.

Calculating the 15th Term of the Sequence

To find the 15th term (a15) of the given arithmetic sequence, we can plug the values into the formula:

a15 14 (15 - 1) x 4

Breaking this down step-by-step:

Therefore, the 15th term of the arithmetic sequence 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70 is 70.

Additional Insight and Practical Uses

Understanding how to find the nth term of an arithmetic sequence is not only useful for academic purposes but also in various real-world applications. For instance, it can help in financial planning, where regular increases or decreases in savings or loans might follow an arithmetic pattern.

Conclusion

By following the step-by-step process and understanding the components of an arithmetic sequence, you can easily find the 15th term of any given arithmetic sequence. The example provided demonstrates a straightforward application of the nth term formula, leading to the final answer of 70. With practice, you'll be able to tackle more complex sequences with confidence.

Keywords

arithmetic sequence, 15th term, common difference