Pattern of Square Tiles

Transcript

Pattern of Square Tiles Let’s look at this pattern of square tiles Here, Number of squares in Stage 1 = 1 Number of squares in Stage 2 = 3 Number of squares in Stage 3 = 5 Number of squares in Stage 4 = 7 So, we can see that Number of tiles increases by 2 in every step Thus, we can write Number of squares in Stage 5 = Number of square in Stage 4 + 2 = 7 + 2 = 9 Similarly, Number of squares in Stage 6 = 9 + 2 = 11 Number of squares in Stage 7 = 11 + 2 = 13 Thus, we can make a table like this Stage 1 2 3 4 5 6 7 Number of the square tiles 1 3 5 7 9 11 13Let’s find Number of squares when Stage = n Now, we can write Number of squares in Stage 2 = 2 × 2 – 1 = 3 Number of squares in Stage 3 = 2 × 3 – 1 = 5 Number of squares in Stage 4 = 2 × 4 – 1 = 7 Thus, we can write Number of squares in Stage n = 2n – 1 Now, let’s answer this Think and Reflect Question from Page 23