Write down the next 5 terms of the following sequences:Name: Date:

Question 1: u_{n+1}=4u_n-4, \qquad u_0=7 |

Question 2: a_{n+1}= {\Large \frac {a_n+16}{2}}, \qquad a_0=4 |

Question 3: x_{n+1}=4x_n+2, \qquad x_0=2 |

Question 4: u_{n+1}= {\Large \frac {u_n}{u_n-1}}, \qquad u_0=6 |

Question 5: a_{n+1}=a_n^2-8a_n-11, \qquad a_0=9 |

Question 6: Show that the equation x^2+6x-23=0 has a solution between \ x=2\ \textrm{and} \ x=3 |

Question 7: Show that the equation x^2-11x-13=0 has a solution between \ x=12\ \textrm{and} \ x=13 |

Question 8: Show that the equation x^2-6x-19=0 has a solution between \ x=8\ \textrm{and} \ x=9 |

Question 9: Show that the equation x^2-9x-3=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

Question 10: Show that the equation x^2+9x-11=0 has a solution between \ x=-11\ \textrm{and} \ x=-10 |

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# Answers

Question 1: u_{1}=24,\qquad u_{2}=92,\qquad u_{3}=364,\qquad u_{4}=1452,\qquad u_{5}=5804 |

Question 2: a_{1}=10,\qquad a_{2}=13,\qquad a_{3}=14.5,\qquad a_{4}=15.25,\qquad a_{5}=15.625 |

Question 3: x_{1}=10,\qquad x_{2}=42,\qquad x_{3}=170,\qquad x_{4}=682,\qquad x_{5}=2730 |

Question 4: u_{1}={\Large \frac {6}{5}},\qquad u_{2}=6,\qquad u_{3}={\Large \frac {6}{5}},\qquad u_{4}=6,\qquad u_{5}={\Large \frac {6}{5}} |

Question 5: a_{1}=-2,\qquad a_{2}=9,\qquad a_{3}=-2,\qquad a_{4}=9,\qquad a_{5}=-2 |

Question 6: f(2)=-7 < 0, f(3)=4 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=2\ \textrm{and} \ x=3 |

Question 7: f(12)=-1 < 0, f(13)=13 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=12\ \textrm{and} \ x=13 |

Question 8: f(8)=-3 < 0, f(9)=8 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=8\ \textrm{and} \ x=9 |

Question 9: f(-1)=7 > 0, f(0)=-3 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-1\ \textrm{and} \ x=0 |

Question 10: f(-11)=11 > 0, f(-10)=-1 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-11\ \textrm{and} \ x=-10 |

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