NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7

Class 7: NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7

The document NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7 is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

Q.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)
 NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7
b)
NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7
c)
NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7
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
NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7
Solution.

(a) From the question it is given that the numbers of segments required to form n digits of the kindNCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7 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 numbers of segments required to form n digits of the kind NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7is (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 numbers of segments required to form n digits of the kindNCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7 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

Q.2. Use the given algebraic expression to complete the table of number patterns.
NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7
Solution.
(i) From the table (2n – 1)
Then, 100th term =?
Where n = 100
= (2 × 100) – 1
= 200 – 1
= 199
(ii) From the table (3n + 2)
5th term =?
Where n = 5
= (3 × 5) + 2
= 15 + 2
= 17
Then, 10th term = ?
Where n = 10
= (3 × 10) + 2
= 30 + 2
= 32
Then, 100th term =?
Where n = 100
= (3 × 100) + 2
= 300 + 2
= 302
(iii) From the table (4n + 1)
5th term = ?
Where n = 5
= (4 × 5) + 1
= 20 + 1
= 21
Then, 10th term = ?
Where n = 10
= (4 × 10) + 1
= 40 + 1
= 41
Then, 100th term = ?
Where n = 100
= (4 × 100) + 1
= 400 + 1
= 401
(iv) From the table (7n + 20)
5th term =  ?
Where n = 5
= (7 × 5) + 20
= 35 + 20
= 55
Then, 10th term = ?
Where n = 10
= (7 × 10) + 20
= 70 + 20
= 90
Then, 100th term = ?
Where n = 100
= (7 × 100) + 20
= 700 + 20
= 720
(v) From the table (n2 + 1)
5th term = ?
Where n = 5
= (52) + 1
= 25+ 1
= 26
Then, 10th term = ?
Where n = 10
= (102) + 1
= 100 + 1
= 101
So the table is completed below.
NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7

The document NCERT Solutions: Algebraic Expressions- 3 Notes | Study Mathematics (Maths) Class 7 - Class 7 is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

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