White squares and black squares are used to form figures that follow a pattern. The first three figures are shown below. How many white squares are used to form Figure 30? Ans: ___

1. Identify the pattern for the total number of squares in Figure $n$

Figure 1 is a $2 \times 2$ grid, so total squares = $2^2 = 4$.
Figure 2 is a $3 \times 3$ grid, so total squares = $3^2 = 9$.
Figure 3 is a $4 \times 4$ grid, so total squares = $4^2 = 16$.
In general, Figure $n$ is an $(n+1) \times (n+1)$ grid, so total squares = $(n+1)^2$.

2. Identify the pattern for the number of black squares in Figure $n$

Figure 1 has 2 black squares.
Figure 2 has 3 black squares.
Figure 3 has 4 black squares.
In general, Figure $n$ has $n+1$ black squares.

3. Formulate the expression for the number of white squares in Figure $n$

Number of white squares = Total squares - Black squares
$= (n+1)^2 - (n+1)$

4. Calculate the number of white squares in Figure 30

For Figure 30, $n = 30$.
Number of white squares $= (30+1)^2 - (30+1)$
$= 31^2 - 31$
$= 961 - 31$
$= 930$