The sum of the first \(n\) terms of an arithmetic sequence is given by \(S_n = \frac{n}{2}(2a + (n-1)d)\). Find the sum of the first 5 terms if \(a = 3\) and \(d = 2\).

["Sum of the First (n) Terms of an Arithmetic Sequence: Find the Sum When (a = 3) and (d = 2)", "The formula for the sum of the first (n) terms of an arithmetic sequence is a fundamental concept in algebra:\n[\nS_n = \frac{n}{2}(2a + (n-1)d)\n]\nwhere:\n- (S_n) is the sum of the first (n) terms,\n- (a) is the first term,\n- (d) is the common difference,\n- (n) is the number of terms.", "This formula offers an efficient way to calculate the total without adding each term individually. It’s especially useful in real-world problems involving patterns, sequences, and financial calculations.", "Let’s apply this formula to find the sum of the first 5 terms of an arithmetic sequence where the first term (a = 3) and the common difference (d = 2).", "Step 1: Plug values into the formula\n[\nS_5 = \frac{5}{2}\left(2(3) + (5-1)(2)\right)\n]", "Step 2: Simplify inside the parentheses\n[\nS_5 = \frac{5}{2}\left(6 + 4 \ imes 2\right) = \frac{5}{2}(6 + 8) = \frac{5}{2}(14)\n]", "Step 3: Calculate the sum\n[\nS_5 = \frac{5 \ imes 14}{2} = \frac{70}{2} = 35\n]", "Conclusion\nThe sum of the first 5 terms of the arithmetic sequence with (a = 3) and (d = 2) is 35.", "Using the standard formula saves time and reduces errors, making it essential for quick calculations in mathematics, physics, engineering, and computer science. Remember:\n[\nS_n = \frac{n}{2}(2a + (n - 1)d)\n]\nis your go-to tool for summing arithmetic sequences.", "---", "Keywords: arithmetic sequence sum formula, (S_n = \frac{n}{2}(2a + (n-1)d)), sum of first 5 terms, arithmetic progression, algebra, problem-solving guide."]