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

Question 1: x_{n+1}=3x_n-6, \qquad x_0=8 |

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

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

Question 4: x_{n+1}=22-x_n, \qquad x_0=27 |

Question 5: a_{n+1}=a_n^2-4a_n-1, \qquad a_0=4 |

Question 6: Show that the equation x^2+4x-1=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 7: Show that the equation x^2+12x-7=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 8: Show that the equation x^2-4x-17=0 has a solution between \ x=6\ \textrm{and} \ x=7 |

Question 9: Show that the equation x^2-5x-2=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

Question 10: Show that the equation x^2-3x-13=0 has a solution between \ x=5\ \textrm{and} \ x=6 |

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# Answers

Question 1: x_{1}=18,\qquad x_{2}=48,\qquad x_{3}=138,\qquad x_{4}=408,\qquad x_{5}=1218 |

Question 2: a_{1}=16,\qquad a_{2}=16,\qquad a_{3}=16,\qquad a_{4}=16,\qquad a_{5}=16 |

Question 3: u_{1}=5,\qquad u_{2}=17,\qquad u_{3}=53,\qquad u_{4}=161,\qquad u_{5}=485 |

Question 4: x_{1}=-5,\qquad x_{2}=27,\qquad x_{3}=-5,\qquad x_{4}=27,\qquad x_{5}=-5 |

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

Question 6: f(0)=-1 < 0, f(1)=4 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

Question 7: f(0)=-7 < 0, f(1)=6 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

Question 8: f(6)=-5 < 0, f(7)=4 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=6\ \textrm{and} \ x=7 |

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

Question 10: f(5)=-3 < 0, f(6)=5 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=5\ \textrm{and} \ x=6 |

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