1. **Problem:** We have groups arriving with the first group having 1 person, the second group 3 people, and each subsequent group having 2 more people than the previous group. Find the number of people in the 20th group. 2. **Formula and Explanation:** This is an arithmetic sequence where the first term $a_1=1$ and the common difference $d=2$ (since each group increases by 2 people). The $n$th term of an arithmetic sequence is given by: $$a_n = a_1 + (n-1)d$$ 3. **Calculation:** $$a_{20} = 1 + (20-1) \times 2 = 1 + 19 \times 2 = 1 + 38 = 39$$ 4. **Answer:** \boxed{39} people will arrive in the twentieth group. This uses the pattern recognition and Polya's problem-solving steps: understanding the problem, devising a plan (arithmetic sequence), carrying out the plan, and looking back (checking the pattern fits the first few groups).