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

Question 1: u_{n+1}=2u_n-9, \qquad u_0=8 |

Question 2: x_{n+1}= {\Large \frac {x_n+12}{2}}, \qquad x_0=8 |

Question 3: a_{n+1}=4a_n+6, \qquad a_0=6 |

Question 4: u_{n+1}= {\Large \frac {70}{u_n}}, \qquad u_0=7 |

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

Question 6: Show that the equation x^2-11x-5=0 has a solution between \ x=11\ \textrm{and} \ x=12 |

Question 7: Show that the equation x^2-4x-23=0 has a solution between \ x=-4\ \textrm{and} \ x=-3 |

Question 8: Show that the equation x^2+3x-17=0 has a solution between \ x=-6\ \textrm{and} \ x=-5 |

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

Question 10: Show that the equation x^2-9x-13=0 has a solution between \ x=-2\ \textrm{and} \ x=-1 |

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# Answers

Question 1: u_{1}=7,\qquad u_{2}=5,\qquad u_{3}=1,\qquad u_{4}=-7,\qquad u_{5}=-23 |

Question 2: x_{1}=10,\qquad x_{2}=11,\qquad x_{3}=11.5,\qquad x_{4}=11.75,\qquad x_{5}=11.875 |

Question 3: a_{1}=30,\qquad a_{2}=126,\qquad a_{3}=510,\qquad a_{4}=2046,\qquad a_{5}=8190 |

Question 4: u_{1}=10,\qquad u_{2}=7,\qquad u_{3}=10,\qquad u_{4}=7,\qquad u_{5}=10 |

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

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

Question 7: f(-4)=9 > 0, f(-3)=-2 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-4\ \textrm{and} \ x=-3 |

Question 8: f(-6)=1 > 0, f(-5)=-7 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-6\ \textrm{and} \ x=-5 |

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

Question 10: f(-2)=9 > 0, f(-1)=-3 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-2\ \textrm{and} \ x=-1 |

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