## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.4

Question 1.

Observe the patterns of shapes of letters formed from line segments of equal lengths:

If n shapes of letters are formed, then write the algebraic expression for the number of line segments required for making these n shapes in each case.

Solution:

2 × 1 + 1 = 2 + 1 = 3

2 × 2 + 1 = 4 + 1 = 5

2 × 3 + 1 = 6 + 1 = 7

2 × n + 1 = 2n + 1 ; n = 1,2, 3,

5 = 3 × 1 + 2 = 3 + 2 = 3 × 1 + 2

8 = 3 × 2 + 2 = 6 + 2 = 3 × 2 + 2

11 = 3 × 3 + 2 = 9 + 2 = 3 × 3 + 2

Generalising, we get 3 × n + 2

Hence, 3n + 2

Question 2.

Observe the pattern of shapes of digits formed from line segment of equal lenghts:

If n shapes of digits are formed, then write the algebraic expression for the number of line segments required for making these n shapes in each case.

Solution:

4 = 3 × 1 + 1 = 3 + 1

7 = 3 × 2 + 1 = 6 + 1

10 = 3 × 3 + 1 = 9 + 1

Generalising, we get 3n+ 1

6 = 5 × 1 + 1

11 = 5 × 2 + 1

16 = 5 × 3 + 1

Generalising, we get 5n + 1

5 × 1 + 2 = 7

5 × 2 + 2 = 12

5 × 3 + 2 = 17

Generalising, we get 5n + 2

Question 3.

If a pattern consists of n shapes formed by line segments of equal lengths and the number of line segments required to make n shapes is given by the algebraic expression:

(i) 2n + 1

(ii) 3n + 1

(iii) 3n + 2

(iv) 5n + 1

(v) 5n + 2

(vi) 4n + 3

then find the number of line segments required to form 5, 10 and 100 shapes in each case.

Solution:

(i) 2n + 1

Taking n = 5, 10, 100, we get

2 × 5 + 1 = 11

2 × 10 + 1 = 21

2 × 100 + 1 = 201

(ii) 3n + 1

Taking n = 5, 10, 100, then we get

3 × 5 + 1 = 16

3 × 10 + 1 = 31

3 × 100 + 1 = 301

(iii) 3n + 2

Taking n = 5, 10, 100, then we get

3 × 5 + 2 = 17

3 × 10 + 2 = 32

3 × 100 + 2 = 302

(iv) 5n + 1

Taking n = 5, 10, 100, then we get

5 × 5 + 1 = 26

5 × 10 + 1 = 51

5 × 100 + 1 = 501

(v) 5n + 2

Taking n = 5, 10, 100, then we get

5 × 5 + 2 = 27

5 × 10 + 2 = 52

5 × 100 + 2 = 502

(vi) 4n + 3

Taking n = 5, 10, 100, then we get

4 × 5 + 3 = 23

5 × 10 + 3 = 53

5 × 100 + 3 = 503