The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is

The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is

Answer Details

To find the sum of the first n terms of an arithmetic progression, we use the formula: Sn = n/2[2a + (n-1)d] where Sn is the sum of the first n terms, a is the first term, and d is the common difference between the terms. In this case, the first term is 5 and the common difference is 6 (since each term is 6 more than the previous one). So, using the formula: Sn = n/2[2(5) + (n-1)(6)] Simplifying, we get: Sn = n/2[10 + 6n - 6] Sn = n/2[6n + 4] Sn = 3n^2 + 2n Therefore, the correct answer is n(3n + 2).