Step-by-step Solution:

\[ \textbf{Given sequence: } 2, \; 6, \; 12, \; 20, \; 30, \; ? \] \[ \textbf{Step 1: Look for a pattern.} \] Observe that the numbers can be expressed as: \[ 2 = 1 \times 2, \quad 6 = 2 \times 3, \quad 12 = 3 \times 4, \quad 20 = 4 \times 5, \quad 30 = 5 \times 6 \] So the general term is: \[ T_n = n \times (n+1), \quad n = 1,2,3,\dots \] \[ \textbf{Step 2: Find the next term.} \] For \(n=6\): \[ T_6 = 6 \times 7 = 42 \] \[ \textbf{Final Answer: } \boxed{42} \]