1. **Problem statement:** We have groups arriving at a 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. We want to find how many people are in the twentieth group. 2. **Formula and explanation:** This is an arithmetic sequence where the first term $a_1 = 1$ and the common difference $d = 2$. The number of people in the $n$th group is given by the formula: $$a_n = a_1 + (n-1)d$$ 3. **Calculate the 20th group:** $$a_{20} = 1 + (20-1) \times 2$$ $$a_{20} = 1 + 19 \times 2$$ $$a_{20} = 1 + 38$$ $$a_{20} = 39$$ 4. **Answer:** The twentieth group will have **39 people**.