These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths 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 watches and 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 6, H, 0.

Answer:

Expression for number of line segments to form ‘n’ figures of the kind 5 is 5n + 1

For 5 figures, like segments = 5×5 + 1 = 25+1 = 26

For. 10 figures, the line segments = 5×10+1 = 50+ = 51

For 100 figures, line segments = 5×100+1 = 500 + 1 = 501

Expression for number of line segments to form ‘n figures of the kind 4 is 3n + 1

For 5 figures, line segment = 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

Expression of number of line segments to form ‘n figures of the kind B is 5n + 2

For 5 figures line segments = 5×5 + 2 = 25+ 2 = 27

For 10 figures line segments = 5x 10 + 2 = 50+ 2 = 52

For 100 figures, line segments = 5x 100 + 2 = 500 + 2 = 502

Question 2.

Use the given algebraic expression to complete the table of number pattern.

Answer:

(i) For the expression 2n – 1

100th term = 2 x 100 – 1

= 200 – 1 = 199

(ii) For the expression 3n + 2

5th term = 3 (5) + 2 = 15 + 2 = 17

10th term = 3 (10) + 2 = 30 + 2 = 32

100th term = 3 (100) + 2 = 300 + 2 = 302

(iii) For the expression 4n + 1

5th term = 4 x 5 +1 = 20+ 1 = 21

10th term = 4 x 10 +1= 40+1 = 41

100th term = 4 x 100 + 1 = 400 + 1 = 401

(iv) For the expression 7n + 20

5th term = 7 x 5 + 20 = 35 + 20 = 55

10th term = 7 x 10 + 20 = 70 + 20 = 90

100th term = 7 x 100 + 20 = 700 + 20 = 720

(v) For the expression n^{2} + 1

5th term = 52 + 1 = 25 + 1 = 26

10th term = 102 + 1 = 100 + 1 = 101