GSEB Solutions Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4

Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 12 Algebraic Expressions Ex 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 watches or 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 form 5, 10, 100 digits of the kind
Solution:
(a)
∵ Expression for number of line segments to form ‘n’ figures of the kind is 5n + 1.
∴ For 5 figures, line segments = 5 x 5 + 1 = 25 + 1= 26
For 10 figures, line segments = 5 x 10 + 1 = 50 + 1 = 51
For 100 figures, line segments = 5 x 100 + 1 = 500 + 1 = 501

(b)
∵ Expression for number of line segments to form ‘n’ figures of the kind is 3n + 1.
∴ For 5 figures, line segments = 3 x 5 + 1 = 15 + 1 = 16
For 10 figures, line segments = 3 x 10 + 1 = 30 + 1 = 31
For 100 figures, line segments = 3 x 100 + 1 = 300 + 1 = 301

(c)
∵ Expression for number of line segments to form ‘n’ figures of the kind is 5n + 2
∴ For 5 figures, line segments = 5 x 5 + 2 = 25 + 2 = 27
For 10 figures, line segments = 5 x 10 + 2 = 50 + 2 = 52
For 100 figures, line segments = 5 x 100 + 2 = 500 + 2 = 502

Question 2.
Use the given algebraic expression to complete the table of number patterns.

Solution:
(i) For the expression 2n – 1
The 100^th term = 2 x 100 – 1
= 200 – 1 = 199

(ii) For the expression 3n + 2,
The 5^th term = 3 x 5 + 2 = 15 + 2= 17
The 10^th term = 3 x 10 + 2 = 30 + 2 = 32
The 100^th term = 3 x 100 + 2 = 300 + 2 = 302

(iii) For the expression An + 1,
The 5^th term = 4 x 5 + 1 = 20 + 1 = 21
The 10^th term = 4 x 10 + 1 = 40 + 1 = 41
The 100^th term = 4 x 100 + 1 = 400 + 1 = 401

(iv) For the expression In + 20,
The 5^th term = 7 x 5 + 20 = 35 + 20 = 55
The 10^th term = 7 x 10 + 20 = 70 + 20 = 90
For 100^th term = 7 x 100 + 20 = 700 + 20 = 720

(v) For the expression n² + 1,
The 5^th term = 5² + 1 = 25 + 1 = 26
The 10^th term = 10² + 1 = 100 + 1 = 101

Note:
1. We can have some patterns with the help of dots also, such as

2. We can have some geometrical patterns as: