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## Algebra: Sequence and Series Test-1

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Question 1 |

The next number of the sequence

3, 5, 9, 17, 33 ……..is:

3, 5, 9, 17, 33 ……..is:

65 | |

60 | |

50 | |

49 |

Question 1 Explanation:

The sequence is 2

^{n}+1 Thus the next term is 6^{th}term. 2^{n}+1 = 2^{6}+1 = 64+1=65. The correct option is (a)Question 2 |

The next term of the sequence$ \displaystyle \frac{1}{2},\,\,3\frac{1}{4},\,\,6,\,\,8\frac{3}{4}........is:$

$ \displaystyle 10\frac{1}{4}$ | |

$ \displaystyle 10\frac{3}{4}$ | |

$ \displaystyle 11\frac{1}{4}$ | |

$ \displaystyle 11\frac{1}{2}$ |

Question 2 Explanation:

The general term is

$ \frac{2+11(n-1)}{4}$

The 5

$latex \frac{46}{4}=\frac{23}{2}=11\frac{1}{2}$

$ \frac{2+11(n-1)}{4}$

The 5

^{th}term will be$latex \frac{46}{4}=\frac{23}{2}=11\frac{1}{2}$

Question 3 |

Find the missing number of the sequence:

“3, 14, 25, 36, 47, ? ”

“3, 14, 25, 36, 47, ? ”

1114 | |

1111 | |

1113 | |

None of these |

Question 3 Explanation:

The general term is 3+11(n-1).

The 6

The 6

^{th}term is 58.Question 4 |

The sum (101+ 102 + 103 + ….. + 200) is equal to:

15000 | |

15025 | |

15050 | |

25000 |

Question 4 Explanation:

The given expression = total of all natural numbers till
200- total of all natural numbers till 100.

$ \begin{array}{l}=\frac{200(200+1)}{2}-\frac{100(100+1)}{2}\\=20100-5050\\=15050\end{array}$

$ \begin{array}{l}=\frac{200(200+1)}{2}-\frac{100(100+1)}{2}\\=20100-5050\\=15050\end{array}$

Question 5 |

Which term of the series 72, 63, 54………..is zero?

11 ^{th} | |

10 ^{th} | |

9 ^{th} | |

8 ^{th} |

Question 5 Explanation:

The general term is 72-9(n-1).

Thus,$ \displaystyle \begin{array}{l}72-9\left( n-1 \right)=0\\=>72=9(n-1)\\=>n-1=8\\=>n=9\end{array}$.

Thus,$ \displaystyle \begin{array}{l}72-9\left( n-1 \right)=0\\=>72=9(n-1)\\=>n-1=8\\=>n=9\end{array}$.

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