A table shows the number of cups (C) for each figure number (n). Figure 1 has 1 cup, Figure 2 has 3 cups, Figure 3 has 5 cups, and Figure 4 has 7 cups. Find a formula for C in terms of n and calculate

The table shows the relationship between the figure number (n) and the number of cups (C).
For Figure 1, Cups = 1
For Figure 2, Cups = 3
For Figure 3, Cups = 5
For Figure 4, Cups = 7

We can see that the number of cups increases by 2 for each subsequent figure. This is an arithmetic progression.
The common difference $d = 2$.
The first term $a = 1$.
The formula for the $n$-th term of an arithmetic progression is $C_n = a + (n-1)d$.
Substituting the values:

$$C_n = 1 + (n-1)2$$ $$C_n = 1 + 2n - 2$$ $$C_n = 2n - 1$$

Using the formula $C_n = 2n - 1$, substitute $n = 15$:

$$C_{15} = 2(15) - 1$$ $$C_{15} = 30 - 1$$ $$C_{15} = 29$$

The number of cups for the 15th figure is $\boxed{\text{29}}$.

Using the formula $C_n = 2n - 1$, substitute $n = 20$:

$$C_{20} = 2(20) - 1$$ $$C_{20} = 40 - 1$$ $$C_{20} = 39$$

The number of cups for the 20th figure is $\boxed{\text{39}}$.