Consider the following designs: (a) Write down the number of squares in design 1, 2, 3, 4, and 5. (b) Determine the number of squares in design n. (c) How many squares are there in design 20?

The first term is $a = 19$.
The common difference is $d = 16 - 19 = -3$.

The nth term is $\boxed{22 - 3n}$ and the 145th term is $\boxed{-413}$.

b) Determine which term of the number pattern equals -389.

The 137th term is $\boxed{137}$.

5. Consider the following designs:

a) Write down the number of squares in design 1, 2, 3, 4, and 5.

Design 1: 1 square
Design 2: 3 squares
Design 3: 5 squares
Design 4: 7 squares

The number of squares forms an arithmetic sequence with a common difference of 2.
So, for design 5, the number of squares is $7 + 2 = 9$.
The number of squares for designs 1, 2, 3, 4, and 5 are $\boxed{1, 3, 5, 7, 9}$.

b) Determine the number of squares in design n.

The first term is $a = 1$ and the common difference is $d = 2$.

The number of squares in design n is $\boxed{2n - 1}$.

c) How many squares are there in design 20?

There are $\boxed{39}$ squares in design 20.