Two separate figures are given below. Each figure shows the first few positions. Class 7

Two separate figures are given below. Each figure shows the first few positions. Class 7

Question 1.

Two separate figures are given below. Each figure shows the first few positions in a sequence of arrangements made with sticks. Identify the pattern and answer the following questions for each figure: Class 7

(a) How many squares are in position number 11 of the sequence?

(b) How many sticks are needed to make the arrangement in position number 11 of the sequence?

(c) Can an arrangement in this sequence be made using exactly 85 sticks? If yes, which position number will it correspond to?

(d) Can an arrangement in this sequence be made using exactly 150 sticks? If yes, which position number will it correspond to?

Solution:

For first figure :

(a) Sequence of squares is 1, 2, 3, ...

So, in 11th position, there will be 11 squares

(b) Sequence of sticks is 6, 9, 12, ...

So, for 11th position, sticks required = 12 × 3 = 36.

(c) No.

(d) Yes, 49th position.

For second figure :

(a) Sequence of squares is 4, 7, 10, 13,'..., (3n + 1)

So, in 11th position, number of squares = 3 × 11 + 1 = 34.

(b) Sequence of sticks is 13, 22, 31, 40, ...

So, for 11th position, number of sticks

= 13 + (11 - 1) × 9

= 13 + 90 = 103.

(c) Yes. Let position be n.

Then, 13 + (n - 1) × 9 = 85 

or 9n - 9 = 72 or n = [latex]\frac {81}{9}[/latex] = 9.

That is at 9th position.

(d) No.