Concept:The series is an arithmetic progression (AP) with first term 6 and common difference 6. We factor out 6 to sum natural numbers.Explanation:Find the number of terms. Last term = 612. Using formula: last = first + (n−1)×d → 612 = 6 + (n−1)×6 → 606 = 6(n−1) → n−1 = 101 → n = 102.Alternatively, divide last term by common difference: 612 ÷ 6 = 102 terms.Now sum = 6 × (1 + 2 + 3 + ... + 102). Sum of first 102 natural numbers = (102 × 103) ÷ 2 = 5253.Multiply by 6: 6 × 5253 = 31518.You can also directly use AP sum formula: Sn = (n ÷ 2) × (first + last) = (102 ÷ 2) × (6 + 612) = 51 × 618 = 31518.Answer:Option A: 31518.