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

Question 1: a_{n+1}=3a_n-5, \qquad a_0=8 |

Question 2: u_{n+1}= {\Large \frac {u_n+14}{2}}, \qquad u_0=4 |

Question 3: x_{n+1}=2x_n+5, \qquad x_0=6 |

Question 4: a_{n+1}= {\Large \frac {36}{a_n}}, \qquad a_0=12 |

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

Question 6: Show that the equation x^2-11x-23=0 has a solution between \ x=12\ \textrm{and} \ x=13 |

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

Question 8: Show that the equation x^2+2x-7=0 has a solution between \ x=-4\ \textrm{and} \ x=-3 |

Question 9: Show that the equation x^2+10x-19=0 has a solution between \ x=-12\ \textrm{and} \ x=-11 |

Question 10: Show that the equation x^2-5x-3=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

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# Answers

Question 1: a_{1}=19,\qquad a_{2}=52,\qquad a_{3}=151,\qquad a_{4}=448,\qquad a_{5}=1339 |

Question 2: u_{1}=9,\qquad u_{2}=11.5,\qquad u_{3}=12.75,\qquad u_{4}=13.375,\qquad u_{5}=13.6875 |

Question 3: x_{1}=17,\qquad x_{2}=39,\qquad x_{3}=83,\qquad x_{4}=171,\qquad x_{5}=347 |

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

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

Question 6: 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 7: f(-1)=2 > 0, f(0)=-1 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-1\ \textrm{and} \ x=0 |

Question 8: f(-4)=1 > 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 9: f(-12)=5 > 0, f(-11)=-8 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-12\ \textrm{and} \ x=-11 |

Question 10: f(-1)=3 > 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 |

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