**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, 100^{th} term =?

Where, n =100

Now,

= (2 × 100) – 1

= 200 – 1

= 199

(ii) According to the table,

(3n + 2)

5^{th} term =?

Where n = 5

= (3 × 5) + 2

= 15 + 2

= 17

Then, 10^{th} term =?

Where, n = 10

= (3 × 10) + 2

= 30 + 2

= 32

Then, 100^{th} term =?

Where n = 100

= (3 × 100) + 2

= 300 + 2

= 302

(iii) According to the table,

(4n + 1)

5^{th} term =?

Where n = 5

= (4 × 5) + 1

= 20 + 1

= 21

Then, 10^{th} term =?

Where n = 10

= (4 × 10) + 1

= 40 + 1

= 41

Then, 100^{th} term =?

Where n = 100

= (4 × 100) + 1

= 400 + 1

= 401

(iv)According to the table,

(7n + 20)

5^{th} term =?

Where n = 5

= (7 × 5) + 20

= 35 + 20

= 55

Then, 10^{th} term =?

Where n = 10

= (7 × 10) + 20

= 70 + 20

= 90

Then, 100^{th} term =?

Where n = 100

= (7 × 100) + 20

= 700 + 20

= 720

(v)According to the table,

(n^{2} + 1)

5^{th} term =?

Where n = 5

= (5^{2}) + 1

= 25+ 1

= 26

Then, 10^{th} term =?

Where n = 10

= (10^{2}) + 1

= 100 + 1

= 101

Hence, the table is completed below.

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