Exercise 12.4 Page: 246

**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.**

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

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

S. No. |
Expression |
Terms |
|||||||||

1^{st} |
2^{nd} |
3^{rd} |
4^{th} |
5^{th} |
… |
10^{th} |
… |
100^{th} |
… |
||

(i) |
2n – 1 |
1 |
3 |
5 |
7 |
9 |
– |
19 |
– |
– |
– |

(ii) |
3n + 2 |
5 |
8 |
11 |
14 |
– |
– |
– |
– |
– |
– |

(iii) |
4n + 1 |
5 |
9 |
13 |
17 |
– |
– |
– |
– |
– |
– |

(iv) |
7n + 20 |
27 |
34 |
41 |
48 |
– |
– |
– |
– |
– |
– |

(v) |
n^{2} + 1 |
2 |
5 |
10 |
17 |
– |
– |
– |
– |
10001 |
– |

**Solution:-**

**(i)** From the table (2n – 1)

Then, 100^{th }term =?

Where n = 100

= (2 × 100) – 1

= 200 – 1

= 199

**(ii)** From 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)** From 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)** From 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)** From 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

So the table is completed below.

S. No. |
Expression |
Terms |
|||||||||

1^{st} |
2^{nd} |
3^{rd} |
4^{th} |
5^{th} |
… |
10^{th} |
… |
100^{th} |
… |
||

(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) |
n^{2} + 1 |
2 | 5 | 10 | 17 | 26 | – | 101 | – | 10001 | – |