The sum of an arithmetic series where the first term is 2, the last term is 50, and there are 25 terms is:

["# The Sum of an Arithmetic Series: First Term 2, Last Term 50, with 25 Terms", "Understanding arithmetic series is fundamental in mathematics, especially in fields like algebra, calculus, and financial modeling. One common problem involves finding the sum of a series with known first term, last term, and number of terms. In this article, we explore the sum of an arithmetic series where the first term is 2, the last term is 50, and there are 25 terms.", "## What is an Arithmetic Series?", "An arithmetic series is the sum of the terms of an arithmetic sequence. An arithmetic sequence is a sequence of numbers where each term increases by a constant difference. For example:\n2, 5, 8, 11, ..., 50", "Here:\n- First term ( a = 2 )\n- Last term ( l = 50 )\n- Number of terms ( n = 25 )", "## Formula for the Sum of an Arithmetic Series", "To compute the sum ( S_n ) of the first ( n ) terms of an arithmetic series, use the formula:", "[\nS_n = \frac{n}{2} \ imes (a + l)\n]", "Where:\n- ( S_n ) is the sum of the first ( n ) terms,\n- ( n ) is the number of terms,\n- ( a ) is the first term,\n- ( l ) is the last term.", "## Applying the Values", "Given:\n- ( a = 2 )\n- ( l = 50 )\n- ( n = 25 )", "Plug these values into the formula:", "[\nS_{25} = \frac{25}{2} \ imes (2 + 50)\n]", "[\nS_{25} = \frac{25}{2} \ imes 52\n]", "[\nS_{25} = 12.5 \ imes 52\n]", "[\nS_{25} = 650\n]", "## Conclusion", "The sum of the arithmetic series starting at 2, ending at 50, with 25 terms is 650. This result is obtained efficiently using the arithmetic series sum formula, making it a powerful tool in solving real-world problems involving cumulative totals, such as savings, loans, and structured data patterns.", "Understanding this concept helps build a strong foundation in mathematical reasoning and supports advanced studies in science, engineering, and economics.", "## Key Takeaways", "- The arithmetic series sum formula: ( S_n = \frac{n}{2} (a + l) )\n- With first term 2, last term 50, and 25 terms, the sum is 650\n- This method applies to any arithmetic sequence when ( a ), ( l ), and ( n ) are known", "Start using this formula to simplify calculations and boost your problem-solving skills in mathematics today!"]