1. The problem presents a pattern of dots where the 1st pattern has 7 dots, the 2nd has 10 dots, and the 3rd has 13 dots. 2. Observe the differences between consecutive terms: $10 - 7 = 3$ and $13 - 10 = 3$. 3. Since the difference is constant, the number of dots follows an arithmetic sequence with common difference $d = 3$. 4. The general form of an arithmetic sequence is $a_n = a_1 + (n-1)d$. 5. Substitute $a_1 = 7$ and $d = 3$ to get the expression: $$a_n = 7 + (n-1) \times 3$$ 6. Simplify the expression: $$a_n = 7 + 3n - 3 = 3n + 4$$ 7. Therefore, the expression for the number of dots in the nth pattern is: $$\boxed{3n + 4}$$