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.
Solution:
(a) According to the question it is given that the number of segments required to form n digits of the given kind are (5n + 1)
Now,
Total required number of segments to form 5 digits = ((5 ×5)+1)
= (25 + 1)
= 26
Total required number of segments to form 10 digits = ((5×10)+1)
= (50 + 1)
= 51
Total required number of segments to form 100 digits = ((5 × 100) + 1)
= (500 + 1)
= 501
(b) According to the question it is given that the number of segments required to form n digits of the given kind (3n + 1)
Now,
Total required number of segments to form 5 digits = ((3 × 5) + 1)
= (15 + 1)
= 16
Total required number of segments to form 10 digits = ((3 × 10) + 1)
= (30 + 1)
= 31
Total required number of segments to form 100 digits = ((3 × 100) + 1)
= (300 + 1)
= 301
(c) According to the question it is given that the number of segments required to form n digits of the given kind (5n + 2)
Now,
Total required number of segments to form 5 digits = ((5 × 5) + 2)
= (25 + 2)
= 27
Total required number of segments to form 10 digits = ((5 × 10) + 2)
= (50 + 2)
= 52
Total required number of segments to form 100 digits = ((5 × 100) + 1)
= (500 + 2)
= 502
2. Use the given algebraic expression to complete the table of number patterns.
Solution:
(i)According to the table,
(2n – 1)
We have to find, 100th term =?
Where, n =100
Now,
= (2 × 100) – 1
= 200 – 1
= 199
(ii) According to 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) According to 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)According to 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)According to 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
Hence, the table is completed below.
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