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

Question 1: u_{n+1}=3u_n-8, \qquad u_0=6 |

Question 2: x_{n+1}= {\Large \frac {x_n+16}{2}}, \qquad x_0=12 |

Question 3: a_{n+1}=3a_n+4, \qquad a_0=2 |

Question 4: u_{n+1}=19-u_n, \qquad u_0=23 |

Question 5: x_{n+1}=x_n^2-6x_n-9, \qquad x_0=7 |

Question 6: Show that the equation x^2-5x-19=0 has a solution between \ x=-3\ \textrm{and} \ x=-2 |

Question 7: Show that the equation x^2+8x-2=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 8: Show that the equation x^2-8x-5=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

Question 9: Show that the equation x^2-6x-11=0 has a solution between \ x=-2\ \textrm{and} \ x=-1 |

Question 10: Show that the equation x^2+11x-23=0 has a solution between \ x=1\ \textrm{and} \ x=2 |

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# Answers

Question 1: u_{1}=10,\qquad u_{2}=22,\qquad u_{3}=58,\qquad u_{4}=166,\qquad u_{5}=490 |

Question 2: x_{1}=14,\qquad x_{2}=15,\qquad x_{3}=15.5,\qquad x_{4}=15.75,\qquad x_{5}=15.875 |

Question 3: a_{1}=10,\qquad a_{2}=34,\qquad a_{3}=106,\qquad a_{4}=322,\qquad a_{5}=970 |

Question 4: u_{1}=-4,\qquad u_{2}=23,\qquad u_{3}=-4,\qquad u_{4}=23,\qquad u_{5}=-4 |

Question 5: x_{1}=-2,\qquad x_{2}=7,\qquad x_{3}=-2,\qquad x_{4}=7,\qquad x_{5}=-2 |

Question 6: f(-3)=5 > 0, f(-2)=-5 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-3\ \textrm{and} \ x=-2 |

Question 7: f(0)=-2 < 0, f(1)=7 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

Question 8: f(-1)=4 > 0, f(0)=-5 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-1\ \textrm{and} \ x=0 |

Question 9: f(-2)=5 > 0, f(-1)=-4 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-2\ \textrm{and} \ x=-1 |

Question 10: f(1)=-11 < 0, f(2)=3 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=1\ \textrm{and} \ x=2 |

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