The pattern in the figures involves increasing numbers of triangles and circles.

Looking at the table, we can observe the following for Figures 1 through 4:

• Number of Triangles:

  • Figure 1: 4
  • Figure 2: 8
  • Figure 3: 12
  • Figure 4: 16
  • We notice an arithmetic pattern, where the number of triangles increases by 4 each time. So, for Figure 5, the number of triangles will be: $16 + 4 = 20$

• Number of Circles:

  • Figure 1: 4
  • Figure 2: 16
  • Figure 3: 36
  • Figure 4: 64
  • The number of circles seems to follow a quadratic pattern, specifically the square of the figure number (squared values: $2^2, 4^2, 6^2, 8^2$). For Figure 5, the number of circles will be: $10^2 = 100$

• Total Number of Triangles and Circles:

  • We can calculate the total number for Figure 5 by adding the values for triangles and circles: $20 + 100 = 120$

Thus, for Figure 5:

• Number of triangles: 20
• Number of circles: 100
• Total number of triangles and circles: 120

Would you like a further breakdown of how the patterns were identified, or do you have any other questions?

Here are 5 related questions to extend this:

1. What is the algebraic expression for the number of triangles in Figure $n$?
2. What is the algebraic formula for the number of circles in Figure $n$?
3. How does the total number of triangles and circles change as $n$ increases?
4. If the pattern continues, what will the number of triangles and circles be in Figure 6?
5. How would the pattern change if the difference between the triangles increased by a number other than 4?

Tip: When dealing with patterns, look for arithmetic (constant difference) or geometric (multiplying factor) progressions to predict future values.