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

Question 1: x_{n+1}=2x_n-6, \qquad x_0=4 |

Question 2: a_{n+1}= {\Large \frac {a_n+8}{2}}, \qquad a_0=10 |

Question 3: u_{n+1}=3u_n+6, \qquad u_0=5 |

Question 4: x_{n+1}= {\Large \frac {x_n}{x_n-1}}, \qquad x_0=6 |

Question 5: a_{n+1}=a_n^2-6a_n-9, \qquad a_0=7 |

Question 6: Show that the equation x^2-2x-19=0 has a solution between \ x=-4\ \textrm{and} \ x=-3 |

Question 7: Show that the equation x^2+2x-13=0 has a solution between \ x=2\ \textrm{and} \ x=3 |

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

Question 9: Show that the equation x^2-11x-23=0 has a solution between \ x=12\ \textrm{and} \ x=13 |

Question 10: Show that the equation x^2-6x-5=0 has a solution between \ x=6\ \textrm{and} \ x=7 |

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# Answers

Question 1: x_{1}=2,\qquad x_{2}=-2,\qquad x_{3}=-10,\qquad x_{4}=-26,\qquad x_{5}=-58 |

Question 2: a_{1}=9,\qquad a_{2}=8.5,\qquad a_{3}=8.25,\qquad a_{4}=8.125,\qquad a_{5}=8.0625 |

Question 3: u_{1}=21,\qquad u_{2}=69,\qquad u_{3}=213,\qquad u_{4}=645,\qquad u_{5}=1941 |

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

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

Question 6: f(-4)=5 > 0, f(-3)=-4 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-4\ \textrm{and} \ x=-3 |

Question 7: f(2)=-5 < 0, f(3)=2 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=2\ \textrm{and} \ x=3 |

Question 8: f(7)=-7 < 0, f(8)=1 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=7\ \textrm{and} \ x=8 |

Question 9: f(12)=-11 < 0, f(13)=3 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=12\ \textrm{and} \ x=13 |

Question 10: f(6)=-5 < 0, f(7)=2 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=6\ \textrm{and} \ x=7 |

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