1. **Problem Statement:** We are running a fund-raising concert. The first group has 1 person, the second group has 3 people, and each subsequent group has 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. **Calculate the 20th term:** $$a_{20} = 1 + (20-1) \times 2$$ $$a_{20} = 1 + 19 \times 2$$ $$a_{20} = 1 + 38$$ $$a_{20} = 39$$ 4. **Interpretation:** The 20th group will have 39 people. **\boxed{39}**