Imagine a straight rope. If it is cut once as shown in the picture, we get 2 pieces. Class 7

Imagine a straight rope. If it is cut once as shown in the picture, we get 2 pieces. Class 7

Question 1.

Imagine a straight rope. If it is cut once as shown in the picture, we get 2 pieces. If the rope is folded once and then cut as shown, we get 3 pieces. Observe the pattern and find the number of pieces if the rope is folded 10 times and cut. What is the expression for the number of pieces when the rope is folded r times and cut? Class 7

Solution:

Pattern is 2, 3, 4, ...

Number of pieces after folding 10 times and then cutting = 10 + 2 = 12.

After folding r times and then cutting, number of pieces = r + 2.

Question 2.

Look at the matchstick pattern below. Observe and identify the pattern. How many matchsticks are required to make 10 such squares. How many are required to make w squares? Class 7

Solution:

Pattern is 4, 7, 10, ..., i.e., 4, 4 + 3, 4 + 2 × 3, 4 + 3 × 3, ...

So, for 10 such squares, matchsticks required = 4 + (10 - 1) × 3 = 31.

For w squares, matchsticks required

= 4 + (w - 1) × 3 = 4 + 3w - 3 = 3w + 1.

Question 3.

Have you noticed how the colours change in a traffic signal? The sequence of colour changes is shown below.

Find the colour at positions 90, 190, and 343. Write expressions to describe the positions for each colour. Class 7

Solution:

Pattern is as follows :

Red: 1, 5, 9, ..., 4n - 3.

Yellow: 2, 4, 6, ..., 2n.

Green: 3, 7, 11, ..., 4n - 1.

Taking 2n = 90, n = 45, a whole number. So, at 90 position, colour will be yellow.

Similarly, at 190 position, colour will be yellow, because 2n = 190 gives 95.

Further, 4n - 1 = 343 ⇒ 4n = 344

⇒ n = [latex]\frac {344}{4}[/latex] = 86, a whole number.

So, at 343 positions colour will be green.