Step-by-step Solution:

\[ \textbf{Given series:} \] \[ (2, 8, 12), \quad (8, 40, 45), \quad (40, 240, 246), \quad ? \] \[ \textbf{Step 1: Look at the pattern.} \] In each triplet: \[ \text{First number} \times \text{Second number} = \text{Third number}. \] \[ 2 \times 6 = 12, \quad 8 \times 5 = 40, \quad 40 \times 6.15 \neq 246 \] Wait — let's carefully check: - First triplet: \( (2, 8, 12) \) → relation: \(2 \times 4 + 4 = 12\). - Second triplet: \( (8, 40, 45) \) → relation: \(8 \times 5 + 5 = 45\). - Third triplet: \( (40, 240, 246) \) → relation: \(40 \times 6 + 6 = 246\). \[ \textbf{So the rule is: Third number} = \text{First number} \times n + n, \] where \(n = 4, 5, 6, \dots\). \[ \textbf{Step 2: Predict next triplet.} \] After \(n = 6\), the next is \(n = 7\). \[ \text{First number of next triplet} = 240, \] \[ \text{Second number} = 240 \times 7 = 1680, \] \[ \text{Third number} = 240 \times 7 + 7 = 1687. \] \[ \textbf{Final Answer: } (240, \; 1680, \; 1687). \] ``` ✅