Question 14 - Figure it out - Page 102 to 105 - Chapter 4 Class 7 - Expressions using Letter-Numbers (Ganita Prakash)

Transcript

Question 14 Observe the pattern below. How many squares will be there in Step 4, Step 10, Step 50? Write a general formula. How would the formula change if we want to count the number of vertices of all the squares?Number of Squares Step 1 has 5 squares. Step 2 has 9 squares. Step 3 has 13 squares. We observe that the pattern is that you start with 1 square and add 4 squares for every step The formula is: Number of squares = 1 + 4s where ‘s' is the number of steps Now, let’s find squares in Step 4, Step 10, Step 50 Number of squares in Step 4: It will have 13 + 4 = 17 squares Number of squares in Step 10: Using the formula below, 1 + 4(10) = 41 squares Number of squares in Step 50: 1 + 4(50) = 201 squares Now, let’s look at vertices Number of Vertices (Assuming Squares share a corner) By counting the vertices in each step, we find a pattern: Step 1: 12 vertices Step 2: 20 vertices Step 3: 28 vertices We observe that the pattern is that the pattern starts at 4 and increases by 8 with each step. The formula is: Number of vertices = 4 + 8s where ‘s' is the number of steps Note (If squares don’t share a corner): If the squares don’t share the corner, our pattern would change Then, By counting the vertices in each step, we find a pattern: Step 1: 20 vertices Step 2: 36 vertices Step 3: 52 vertices We can also find out number of vertices from number of squares Since each square has 4 vertices Number of vertices = 4 × Number of squares = 4 × (1 + 4s) = 4 + 16s