1. **State the problem:** We are given the sequence 2, 6, 12, 20, 30 and asked to analyze it. 2. **Identify the pattern:** Notice the terms: 2, 6, 12, 20, 30. 3. **Check if the terms fit a formula:** Let's try to express the $n$th term $a_n$ in terms of $n$. 4. **Calculate the terms with $n=1,2,3,4,5$:** - $a_1 = 2$ - $a_2 = 6$ - $a_3 = 12$ - $a_4 = 20$ - $a_5 = 30$ 5. **Try the formula $a_n = n(n+1)$:** - For $n=1$, $1 \times 2 = 2$ ✓ - For $n=2$, $2 \times 3 = 6$ ✓ - For $n=3$, $3 \times 4 = 12$ ✓ - For $n=4$, $4 \times 5 = 20$ ✓ - For $n=5$, $5 \times 6 = 30$ ✓ 6. **Conclusion:** The $n$th term of the sequence is given by the formula $$a_n = n(n+1)$$ This means each term is the product of $n$ and its successor $n+1$. 7. **Additional insight:** This sequence represents the sequence of pronic numbers, which are the product of two consecutive integers. **Final answer:** The formula for the sequence is $a_n = n(n+1)$.