The nth term of an arithmetic sequence is given by: first term + (n - 1) × common difference.

["# Understanding the nth Term of an Arithmetic Sequence: Formula, Examples, and Applications", "Arithmetic sequences are fundamental concepts in algebra, widely used in mathematics, finance, computer science, and everyday problem-solving. Whether you're tracking savings, analyzing patterns, or solving math problems, knowing how to find the nth term of an arithmetic sequence is essential. This article explains the formula, how it works, and includes practical examples to help you master this core concept.", "---", "## What is an Arithmetic Sequence?", "An arithmetic sequence is a ordered list of numbers (called terms) where each term differs from the previous one by a constant value known as the common difference. For example, the sequence 3, 7, 11, 15, … has a first term of 3 and a common difference of 4.", "---", "## The nth Term Formula: How It Works", "The nth term of an arithmetic sequence is found using the formula:", "$$\na_n = a + (n - 1)d\n$$", "Where:\n- $a_n$ = the nth term\n- $a$ = first term of the sequence\n- $d$ = common difference\n- $n$ = term number (a positive integer)", "### What Each Components Means:", "- First term ($a$): The starting value of the sequence.\n- Common difference ($d$): The constant added to each term to get the next.\n- Term number ($n$): The position of the term in the sequence (e.g., 1st, 2nd, 3rd, ...).", "Because the sequence progresses by adding $d$ repeatedly, the nth term is simply the first term increased by $(n - 1)$ times the common difference.", "---", "## Step-by-Step Example", "Let’s apply the formula to solve for the 5th term of an arithmetic sequence with:\n- $a = 2$\n- $d = 3$", "Step 1: Identify $n = 5$\nStep 2: Use the formula:", "$$\na_5 = 2 + (5 - 1) \ imes 3 = 2 + 4 \ imes 3 = 2 + 12 = 14\n$$", "✅ The 5th term is 14.", "---", "## Practical Applications of the nth Term Formula", "Understanding the nth term helps in multiple real-world contexts:", "- Savings Plans: If you save a fixed amount each month (e.g., $20), your total savings after $n$ months follow an arithmetic sequence.\n- Monthly Rent Increases: If rent rises by the same amount each year, the future value is calculated with the nth term formula.\n- Problem Solving: In math competitions or daily life, determining unknown values in patterns becomes straightforward.", "---", "## Tips for Using the Formula", "- Ensure consistent sign for $d$: Negative common differences decrease the sequence.\n- Remember $n$ must be a positive integer (1, 2, 3,...).\n- Practice rewriting terms to test your understanding — e.g., find $a_1, a_4, a_{10}$.", "---", "## Conclusion", "The formula $a_n = a + (n - 1)d$ is a powerful tool for finding any term in an arithmetic sequence instantly. By identifying the first term ($a$) and common difference ($d$) and recognizing that $n$ counts the term’s position, you can effortlessly calculate positioning in number patterns. Mastering this concept empowers you to solve problems across science, finance, and technology with ease.", "### Key Takeaway:\nThe nth term of an arithmetic sequence is given by: first term + (n – 1) × common difference.", "---", "Start practicing today — calculate the 1st, 10th, 50th, or any term in a sequence using this simple yet powerful formula!"]