QB_PH_GA_021: Analytical & Spatial Aptitude

Find the missing number in the sequence: $2, \; 6, \; 12, \; 20, \; 30, \; 42, \; ?$

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Pattern Recognition Method 1 (Successive Differences)**: $6 - 2 = 4$ $12 - 6 = 6$ $20 - 12 = 8$ $30 - 20 = 10$ $42 - 30 = 12$ The difference sequence increases by $+2$ each step. Next difference: $12 + 2 = 14$. $\text{Next Term} = 42 + 14 = 56$ 2. **Pattern Recognition Method 2 (Factor Product $n(n+1)$)**: $1 \times 2 = 2, \; 2 \times 3 = 6, \; 3 \times 4 = 12, \; 4 \times 5 = 20, \; 5 \times 6 = 30, \; 6 \times 7 = 42$ $\text{Term 7} = 7 \times 8 = 56$ 3. **Official Value**: 56.