NCERT Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.4

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 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)

is (5n + 1)
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)

is (3n + 1)
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)

is (5n + 2)
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

Question 2: Use the given algebraic expression to complete the table of number patterns.
Answer:
(i) 2n – 1
Then, 100th term =?
n = 100
= (2 × 100) – 1
= 200 – 1
= 199

(ii) 3n + 2
5th term =?
n = 5
= (3 × 5) + 2
= 15 + 2
= 17
10th term =?
n = 10
= (3 × 10) + 2
= 30 + 2
= 32
100th term =?
n = 100
= (3 × 100) + 2
= 300 + 2
= 302

(iii) 4n + 1
5th term =?
n = 5
= (4 × 5) + 1
= 20 + 1
= 21
10th term =?
n = 10
= (4 × 10) + 1
= 40 + 1
= 41
100th term =?
n = 100
= (4 × 100) + 1
= 400 + 1
= 401

(iv) 7n + 20
5th term =?
n = 5
= (7 × 5) + 20
= 35 + 20
= 55
10th term =?
n = 10
= (7 × 10) + 20
= 70 + 20
= 90
100th term =?
n = 100
= (7 × 100) + 20
= 700 + 20
= 720

(v) n2 + 1
5th term =?
n = 5
= (52) + 1
= 25+ 1
= 26
10th term =?
n = 10
= (102) + 1
= 100 + 1
= 101

S. No.

Expression

Terms

1st

2nd

3rd

4th

5th

10th

100th

(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

No comments:

Post a Comment

Also read!

Class 6 Solutions

• Class 7

Class 7 Computer Kips Solutions
Class 7 Gul Mohar English Solutions
English Grammar Class 7
English Writing Skills Class 7
Class 7 Map Pointing Solutions
Class 7 NCERT Civics Solutions
Class 7 NCERT Civics Notes
Class 7 NCERT Civics Extra Questions
Class 7 NCERT Geography Solutions
Class 7 NCERT Geography Notes
Class 7 NCERT Geography Extra Questions
Class 7 NCERT History Solutions
Class 7 NCERT History Notes
Class 7 NCERT History Extra Questions
Class 7 NCERT Maths Solutions
Class 7 NCERT Science Solutions
Class 7 NCERT Science Notes
Class 7 NCERT Science Extra Questions

• Class 8

Class 8 Kips Artificial Intelligence Solutions
Class 8 Gul Mohar English Solutions
English Grammar Class 8
English Writing Skills Class 8
Class 8 Map Pointing Solutions
Class 8 NCERT Civics Solutions
Class 8 NCERT Civics Notes
Class 8 NCERT Civics Extra Questions
Class 8 NCERT Geography Solutions
Class 8 NCERT Geography Notes
Class 8 NCERT Geography Extra Questions
Class 8 NCERT History Solutions
Class 8 NCERT History Notes
Class 8 NCERT History Extra Questions
Class 8 NCERT Maths Solutions
Class 8 NCERT Science Solutions
Class 8 NCERT Science Notes
Class 8 NCERT Science Extra Questions
Class 8 NCERT Science Exemplar
Class 8 NCERT Science MCQs

Class 9 Solutions

• Class 10

Class 10 Kips Artificial Intelligence Solutions
Class 10 NCERT English Solutions
→ Class 10 Map Pointing Solutions
Class 10 NCERT Civics Solutions
Class 10 NCERT Civics Notes
Class 10 NCERT Civics Extra Questions
Class 10 NCERT Geography Solutions
Class 10 NCERT Geography Notes
Class 10 NCERT Geography Extra Questions
Class 10 NCERT History Solutions
→ Class 10 NCERT History Notes
Class 10 NCERT History Extra Questions
Class 10 NCERT Maths Solutions
Class 10 NCERT Science Solutions
Class 10 NCERT Science Notes
Class 10 NCERT Science Extra Questions

• Computer languages
Python Basics

• Extra Activities
Extra Activities

• Extra Knowledge
Extra Information
General Knowledge
Historical Places in India
Latest technology
Physical Sciences
Facts

• Mathematics quick links
Mathematical Terms
Maths Tricks

CONTACT US