Question

figure 1
figure 2
figure 3
figure 4
figure 5
mp structure draw the missing figure in the pattern. explain the pattern.

Explanation:

Step1: Analyze the pattern of the number of squares

Figure 1 has 1 square. Figure 2 has 3 squares. Figure 3 has 5 squares. Figure 5 has 9 squares. The number of squares follows an arithmetic - sequence pattern where the number of squares in the \(n\)th figure can be represented by the formula \(a_{n}=2n - 1\) (for \(n = 1,2,\cdots\)). For \(n = 4\), \(a_{4}=2\times4 - 1=7\).

Step2: Analyze the shape pattern

Looking at the shape, each new figure extends either the horizontal or vertical 'arm' of the L - shape. Figure 1 is a single square. Figure 2 extends one square to the right and one down. Figure 3 extends the horizontal 'arm' by one more square. Following the alternating extension pattern (first vertical then horizontal), for Figure 4, we extend the vertical 'arm' of the L - shape (starting from Figure 3's structure) by one square so that the total number of squares is 7.

Answer:

The missing Figure 4 should have 7 squares in an L - shape where the vertical 'arm' is one square longer than in Figure 3. (It can be drawn as an L - shape with 4 squares in one 'arm' and 3 squares in the other 'arm' to make a total of 7 squares)