👉 The submitted math problem involves finding the sum of the first \( n \) terms of an arithmetic series, where the first term is 3 and the common difference is 4. The formula for the sum \( S_n \) of the first \( n \) terms of an arithmetic series is given by \( S_n = \frac{n}{2} [2a + (n-1)d] \), where \( a \) is the first term and \( d \) is the common difference. Here, \( a = 3 \) and \( d = 4 \). Plugging these values into the formula gives \( S_n = \frac{n}{2} [2(3) + (n-1)(4)] = \frac{n}{2} [6 + 4n - 4] = \frac{n}{2} (4n + 2) = n(2n + 1) \). This simplifies to \( S_n = 2n^2 + n \), which is the sum of the first \( n \) terms of the series.
