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

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

1st | 2nd | 3 | 4th | 5th | … | 10th | … | 100th | … | ||

(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 | 5 | 10 | 17 | - | - | - | - | 10001 |

(i)Expression = 2n - 1

100^{th} term (i.e. n = 100)

= 2(100) - 1

= 200 - 1

= 199

(ii)Expression = 3n + 2

5^{th} term( i.e. n = 5)

= 3(5) + 2

= 15 + 2

= 17

10^{th} terms(i.e.. n =10)

=3(10) + 2

=30 + 2

= 32

100^{th} term( i.e. n = 100)

=3(100) + 2

= 300 + 2

= 302

(iii)Expression = 4n + 1

5^{th} term( i.e. n = 5)

= 4(5) + 1

= 20 + 1

= 21

10^{th} terms(i.e.. n =10)

=4(10) + 1

=40 + 1

= 41

100^{th} term( i.e. n = 100)

=4(100) + 1

= 400 + 1

= 401

(iv)Expression = 7n + 20

5^{th} term( i.e. n = 5)

= 7(5) + 20

= 35 + 20

= 55

10^{th} terms(i.e.. n =10)

=7(10) + 20

=70 + 20

= 90

100^{th} term( i.e. n = 100)

=7(100) + 20

= 700 + 20

= 720

(ii)Expression = n^{2} + 1

5^{th} term( i.e. n = 5)

= (5)^{2} + 1

= 25 + 1

= 26

10^{th} terms(i.e.. n =10)

=(10)^{2} + 1

=100 + 1

= 101

So the Table is

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

1st | 2nd | 3 | 4th | 5 | … | 10th | … | 100th | … | ||

(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 | 5 | 10 | 17 | 26 | - | 101 | - | 10001 |

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