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NCERT solution class 7 chapter 12 Algebraic expressions 12.4 mathematics

EXERCISE 12.4


Page No 246:

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.

(a)

(b)

(c)

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) It is given that the number of segments required to form n digits of the kind

 is (5n + 1).

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

= 25 + 1 = 26

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

= 50 + 1 = 51

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

= 500 + 1 = 501

(b) It is given that the number of segments required to form n digits of the kind  is (3n + 1).

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

= 15 + 1 = 16

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

= 30 + 1 = 31

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

= 300 + 1 = 301

(c)It is given that the number of segments required to form n digits of the kind  is (5n + 2).

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

= 25 + 2 = 27

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

= 50 + 2 = 52

Number of segments required to form 100 digits = (5 × 100 + 2)

= 500 + 2 = 502

Page No 247:

Question 2:

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

S. No

Expression

Terms

1st

2nd

3rd

4th

5th

10th

100th

(i)

2n − 1

1

3

5

7

9

19

(ii)

3n + 2

2

5

8

11

(iii)

4n + 1

5

9

13

17

(iv)

7n + 20

27

34

41

48

(v)

n2 + 1

2

5

10

17

10, 001

Answer:

The given table can be completed as follows.

S.No.

Expression

Terms

1st

2nd

3rd

4th

5th

10th

100th

(i)

2n − 1

1

3

5

7

9

19

199

(ii)

3n + 2

2

5

8

11

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

10,001-

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