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

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

Question 2: a_{n+1}= {\Large \frac {a_n+14}{2}}, \qquad a_0=6 |

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

Question 4: u_{n+1}= {\Large \frac {55}{u_n}}, \qquad u_0=11 |

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

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

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

Question 8: Show that the equation x^2-9x-3=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

Question 9: Show that the equation x^2+10x-2=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

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}=-3,\qquad u_{2}=-15,\qquad u_{3}=-39,\qquad u_{4}=-87,\qquad u_{5}=-183 |

Question 2: a_{1}=10,\qquad a_{2}=12,\qquad a_{3}=13,\qquad a_{4}=13.5,\qquad a_{5}=13.75 |

Question 3: x_{1}=15,\qquad x_{2}=51,\qquad x_{3}=159,\qquad x_{4}=483,\qquad x_{5}=1455 |

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

Question 5: a_{1}=-1,\qquad a_{2}=8,\qquad a_{3}=-1,\qquad a_{4}=8,\qquad a_{5}=-1 |

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

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

Question 8: 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 9: f(0)=-2 < 0, f(1)=9 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

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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