NCERT · Class 7 · Maths

Chapter 10: Algebraic Expressions

Practice each question, then open the answer or worked solution.

Exercise 12.4

Textbook page 246 · 2 questions

Q1Written answer

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

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Worked solution

Solution:-

(a) From the question, it is given that the number of segments required to form n digits of the kind
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 8 is (5n + 1)

Then,

The number of segments required to form 5 digits = ((5 × 5) + 1)

= (25 + 1)

= 26

The number of segments required to form 10 digits = ((5 × 10) + 1)

= (50 + 1)

= 51

The number of segments required to form 100 digits = ((5 × 100) + 1)

= (500 + 1)

= 501

(b) From the question, it is given that the number of segments required to form n digits of the kind
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 9 is (3n + 1)

Then,

The number of segments required to form 5 digits = ((3 × 5) + 1)

= (15 + 1)

= 16

The number of segments required to form 10 digits = ((3 × 10) + 1)

= (30 + 1)

= 31

The number of segments required to form 100 digits = ((3 × 100) + 1)

= (300 + 1)

= 301

(c) From the question, it is given that the number of segments required to form n digits of the kind
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 10 is (5n + 2)

Then,

The number of segments required to form 5 digits = ((5 × 5) + 2)

= (25 + 2)

= 27

The number of segments required to form 10 digits = ((5 × 10) + 2)

= (50 + 2)

= 52

The number of segments required to form 100 digits = ((5 × 100) + 1)

= (500 + 2)

= 502

Q2Written answer

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

S. No.	Expression	Terms
S. No.	Expression	1^st	2^nd	3^rd	4^th	5^th	…	10^th	…	100^th	…
(i)	2n – 1	1	3	5	7	9	–	19	–	–	–
(ii)	3n + 2	5	8	11	14	–	–	–	–	–	–
(iii)	4n + 1	5	9	13	17	–	–	–	–	–	–
(iv)	7n + 20	27	34	41	48	–	–	–	–	–	–
(v)	n² + 1	2	5	10	17	–	–	–	–	10001	–

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Worked solution

Solution:-

(i) From the table (2n – 1)

Then, 100^thterm =?

Where n = 100

= (2 × 100) – 1

= 200 – 1

= 199

(ii) From the table (3n + 2)

5^thterm =?

Where n = 5

= (3 × 5) + 2

= 15 + 2

= 17

Then, 10^thterm =?

Where n = 10

= (3 × 10) + 2

= 30 + 2

= 32

Then, 100^thterm =?

Where n = 100

= (3 × 100) + 2

= 300 + 2

= 302

(iii) From the table (4n + 1)

5^thterm =?

Where n = 5

= (4 × 5) + 1

= 20 + 1

= 21

Then, 10^thterm =?

Where n = 10

= (4 × 10) + 1

= 40 + 1

= 41

Then, 100^thterm =?

Where n = 100

= (4 × 100) + 1

= 400 + 1

= 401

(iv) From the table (7n + 20)

5^thterm =?

Where n = 5

= (7 × 5) + 20

= 35 + 20

= 55

Then, 10^thterm =?

Where n = 10

= (7 × 10) + 20

= 70 + 20

= 90

Then, 100^thterm =?

Where n = 100

= (7 × 100) + 20

= 700 + 20

= 720

(v) From the table (n² + 1)

5^thterm =?

Where n = 5

= (5²) + 1

= 25+ 1

= 26

Then, 10^thterm =?

Where n = 10

= (10²) + 1

= 100 + 1

= 101

So, the table is completed below.

S. No.	Expression	Terms
S. No.	Expression	1^st	2^nd	3^rd	4^th	5^th	…	10^th	…	100^th	…
(i)	2n – 1	1	3	5	7	9	–	19	–	199	–
(ii)	3n + 2	5	8	11	14	17	–	32	–	302	–
(iii)	4n + 1	5	9	13	17	21	–	41	–	401	–
(iv)	7n + 20	27	34	41	48	55	–	90	–	720	–
(v)	n² + 1	2	5	10	17	26	–	101	–	10001	–

Disclaimer:

Dropped Topics – 12.6 Addition and subtraction of algebraic expressions, 12.8 Using algebraic expressions–formulas and rules

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Chapter 10: Algebraic Expressions

Exercise 12.4