Find the sum of the first 8 terms of the arithmetic sequence where the first term is 5 and the common difference is 3.
["# How to Find the Sum of the First 8 Terms of an Arithmetic Sequence\n(With Step-by-Step Example: First Term = 5, Common Difference = 3)", "When it comes to arithmetic sequences, calculating the sum of the first few terms is a fundamental skill—especially in math education, careers in engineering, data analysis, and more. In this SEO-optimized guide, we’ll explore how to efficiently find the sum of the first 8 terms of a specific arithmetic sequence where the first term is 5 and the common difference is 3.", "## What Is an Arithmetic Sequence?", "An arithmetic sequence is a list of numbers in which each term after the first is obtained by adding a constant difference. The formula for the n-th term is:", "[\na_n = a_1 + (n - 1)d\n]", "Where:\n- (a_1) = first term\n- (d) = common difference\n- (n) = term number\n- (a_n) = n-th term", "The sum of the first (n) terms, denoted (S_n), is given by:", "[\nS_n = \frac{n}{2} \ imes (a_1 + a_n)\n]", "Or equivalently,\n[\nS_n = \frac{n}{2} \ imes [2a_1 + (n - 1)d]\n]", "---", "## Step-by-Step: Sum of the First 8 Terms", "Given:\n- First term ((a_1)) = 5\n- Common difference ((d)) = 3\n- Number of terms ((n)) = 8", "### Step 1: Find the 8th term ((a_8))", "Using the n-th term formula:\n[\na_8 = a_1 + (8 - 1) \cdot d = 5 + 7 \cdot 3 = 5 + 21 = 26\n]", "### Step 2: Apply the sum formula", "[\nS_8 = \frac{8}{2} \ imes (a_1 + a_8) = 4 \ imes (5 + 26) = 4 \ imes 31 = 124\n]", "Alternatively,\n[\nS_8 = \frac{8}{2} \ imes [2 \cdot 5 + (8 - 1) \cdot 3] = 4 \ imes [10 + 21] = 4 \ imes 31 = 124\n]", "---", "## Why This Method Matters (SEO Keywords Included)", "- Arithmetic sequence sum formula: The most efficient way to calculate (S_n) without listing all terms.\n- Mathematics tutorials: Clear, step-by-step arithmetic is essential for students and lifelong learners.\n- First 8 terms summation: A common query in math education—ideal for homework help or exam prep.\n- Common difference applications: Understanding how (d) impacts sequences builds strong foundational skills.", "---", "## Conclusion", "The sum of the first 8 terms of the arithmetic sequence starting at 5 with a common difference of 3 is 124. Using the sum formula not only speeds up calculation but also strengthens conceptual understanding. Whether you're solving math problems, preparing for a test, or teaching arithmetic sequences, mastering this method is both practical and powerful.", "---", "Key Takeaways:\n- Use (S_n = \frac{n}{2}[2a_1 + (n - 1)d]) for quick sums.\n- Always confirm the 8th term before applying the formula.\n- This technique applies universally across math disciplines.", "---", "Try it now! Use the formula with any arithmetic sequence to boost your efficiency and confidence in math. Search “first 8 terms arithmetic sum” for more practice problems and video tutorials to reinforce your learning.", "---", "Meta Summary:\nSEO-optimized article explaining how to find the sum of the first 8 terms in the arithmetic sequence starting at 5 with common difference 3, using step-by-step calculations, formulas, and educational relevance. Ideal for students, educators, and math enthusiasts seeking clarity and efficiency."]
