Haryana State Board HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 Textbook Exercise Questions and Answers.
Haryana Board 7th Class Maths Solutions Chapter 12 Algebraic Expressions Exercise 12.4
Question 1.
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic calculators.
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to from 5, 10, 100 digits of the kind
Solution:
(a) If n = 4
∴ 5n + 1 = 5 × 4 + 1 = 20 + 1 = 21
If n = 5
∴ 5n + 1 = 5 × 5 + 1 = 25 + 1 = 26
If n = 10
∴ 5n + 1 = 5 × 10 + 1 = 50 + 1 = 51
If n = 100
∴ 5n + 1 = 5 × 100 + 1 = 500 + 1 = 501
(b) n = 4
3n + 1 = 3 × 4 + 1 = 12 + 1 = 13
If n = 5,
3n + 1 = 3 × 5 + 1 = 15 + 1 = 16
If n = 10
3n + 1 = 3 × 10 + 1 = 30 + 1 = 31
If n = 100
3n + 1 = 3 × 100 + 1 = 300 + 1 = 301
(c) If n = 4
5n+ 2 = 5 × 4 + 2 = 20 + 2 = 22
If n = 5
5n + 2= 5 × 5 + 2 = 25 + 2 = 27
If n = 10
5n + 2 = 5 × 10 + 2 =50+ 2 = 52
If n = 100
5n + 2 = 5 × 100 + 2 =500 + 2 = 502
Question 2.
Use the given algebraic expression to complete the table of number patterns (sequences):
Solution:
(1) If n = 100
2n – 1 = 2 × 100 – 1 = 200 – 1 = 199
(2) If n = 5
3n + 2 = 3 × 5 + 2 = 15 + 2 = 17
If n = 10
3n + 2 = 3 × 10 + 2 = 30 + 2 = 32
If n = 100
3n + 2 = 3 × 100 + 2 = 300 + 2 = 302
(3) If n = 5
4n + 1 = 4 × 5 + 1 = 20 + 1 = 21
If n = 10
4n + 1 = 4 × 10 + 1 = 40 + 1 = 41
If n = 100
4n + 1 = 4 × 100 + 1 = 400 + 1 = 401
(4) If n = 5, 7n + 20 = 7 × 5 + 20
= 35 + 20 = 55
If n = 10, 7n + 20 = 7 × 10 + 20
= 70 + 20 = 90
If n = 100, 7n + 20 = 7 × 100 + 20
= 700 + 20 = 720
(5) If n = 5, n2 + 1 = 5 × 5 + 1
= 25 + 1 = 26
If n = 10, + n2 = 10 × 10 + 1
= 100 + 1 = 101