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

Question 1: a_{n+1}=2a_n-6, \qquad a_0=8 |

Question 2: u_{n+1}= {\Large \frac {u_n+8}{2}}, \qquad u_0=14 |

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

Question 4: a_{n+1}= {\Large \frac {a_n}{a_n-1}}, \qquad a_0=6 |

Question 5: u_{n+1}=u_n^2-u_n-9, \qquad u_0=3 |

Question 6: Show that the equation x^2+11x-7=0 has a solution between \ x=-12\ \textrm{and} \ x=-11 |

Question 7: Show that the equation x^2-10x-13=0 has a solution between \ x=11\ \textrm{and} \ x=12 |

Question 8: Show that the equation x^2-9x-17=0 has a solution between \ x=-2\ \textrm{and} \ x=-1 |

Question 9: Show that the equation x^2+5x-2=0 has a solution between \ x=-6\ \textrm{and} \ x=-5 |

Question 10: Show that the equation x^2-6x-11=0 has a solution between \ x=7\ \textrm{and} \ x=8 |

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# Answers

Question 1: a_{1}=10,\qquad a_{2}=14,\qquad a_{3}=22,\qquad a_{4}=38,\qquad a_{5}=70 |

Question 2: u_{1}=11,\qquad u_{2}=9.5,\qquad u_{3}=8.75,\qquad u_{4}=8.375,\qquad u_{5}=8.1875 |

Question 3: x_{1}=8,\qquad x_{2}=18,\qquad x_{3}=38,\qquad x_{4}=78,\qquad x_{5}=158 |

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

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

Question 6: f(-12)=5 > 0, f(-11)=-7 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-12\ \textrm{and} \ x=-11 |

Question 7: f(11)=-2 < 0, f(12)=11 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=11\ \textrm{and} \ x=12 |

Question 8: f(-2)=5 > 0, f(-1)=-7 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-2\ \textrm{and} \ x=-1 |

Question 9: f(-6)=4 > 0, f(-5)=-2 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-6\ \textrm{and} \ x=-5 |

Question 10: f(7)=-4 < 0, f(8)=5 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=7\ \textrm{and} \ x=8 |

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