Question:** Find the sum of the first 10 terms of an arithmetic sequence where the first term is 3 and the common difference is 5.
["Title: How to Calculate the Sum of the First 10 Terms in an Arithmetic Sequence (Step-by-Step Explanation)", "Meta Description: Learn how to find the sum of the first 10 terms in an arithmetic sequence with first term 3 and common difference 5. Step-by-step math solution for students and math enthusiasts.", "---", "### Understanding Arithmetic Sequences\nAn arithmetic sequence is a sequence of numbers where each term increases by a constant difference. This difference is called the common difference.", "In this example:\n- First term ((a_1)) = 3\n- Common difference ((d)) = 5\n- Number of terms ((n)) = 10", "---", "### Formula for Sum of an Arithmetic Sequence\nThe sum (S_n) of the first (n) terms of an arithmetic sequence is given by:\n[\nS_n = \frac{n}{2} \ imes (2a_1 + (n - 1)d)\n]\nAlternatively,\n[\nS_n = \frac{n}{2} \ imes (a_1 + a_n)\n]\nwhere (a_n) is the (n)-th term.", "---", "### Step 1: Find the 10th Term ((a_{10}))\nTo use the sum formula, we first calculate the 10th term in the sequence:\n[\na_n = a_1 + (n - 1) \ imes d\n]\nSubstitute (n = 10):\n[\na_{10} = 3 + (10 - 1) \ imes 5 = 3 + 9 \ imes 5 = 3 + 45 = 48\n]", "---", "### Step 2: Apply the Sum Formula\nNow use the sum formula:\n[\nS_{10} = \frac{10}{2} \ imes (3 + 48) = 5 \ imes 51 = 255\n]\nAlternatively:\n[\nS_{10} = \frac{10}{2} \ imes (2 \ imes 3 + 9 \ imes 5) = 5 \ imes (6 + 45) = 5 \ imes 51 = 255\n]", "---", "### Final Answer\nThe sum of the first 10 terms of this arithmetic sequence is 255.", "---", "### Why This Matters\nUnderstanding how to calculate term sums in arithmetic sequences is essential in algebra, financial planning (like compound interest), and data analysis. Whether for homework, exams, or real-world math problems, mastering this formula empowers you with a fundamental mathematical tool.", "---", "Keywords: arithmetic sequence sum, first 10 terms sum, arithmetic series formula, find arithmetic sum, step-by-step math tutorial, common difference, sum of terms formula", "---", "Summary: By applying the arithmetic sequence sum formula and computing the 10th term, we found the total sum in just two simple steps—proof that a little math insight goes a long way!"]
