RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions 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

Answer:
(a)

∵ Expression for number of line segments to form ‘n figures of the find

5n + 1.
∴ For five figures, line segments = 5 × 5 + 1 = 25 + 1 = 26
For 10 figures, line segments = 5 × 10 + 1 = 50 + 1 = 51
For 100 figures, line segments = 5 × 100 + 1 = 500 + 1 = 501

(b)

∵ Expression for number of line segments to form n figures of the find

3n + 1.
∴ For 5 figures, line segments = 3 × 5 + 1 = 15 + 1 = 16
For 10 figures, line segments= 3 × 10 + 1 = 30 + 1 = 31
For 100 figures, line segments = 3 × 100 + 1 = 300 + 1 = 301

(c)

∵ Expression for number of line segments to form ‘n’ figures of the kind

5n + 2.
For 5 figures, line segments = 5 × 5 + 2 = 25 + 2 = 27
For 10 figures, line segments = 5 × 10 + 2 = 50 + 2 = 52
For 100 figures, line segments = 5 × 100 + 2 = 500 + 2 = 502

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

Answer:
(i) For the expression 2n - 1
The 100^th term = 2 × 100 - 1
= 200 - 1 = 199

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

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

(iv) For the expression 7n + 20
The 5^th term = 7 × 5 + 20 = 35 + 20 = 55
The 10^th term = 7 × 10 + 20 = 70 + 20 = 90
The 100^th term = 7 × 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
The 100^th term = 100² + 1 = 10000 + 1 = 10001