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

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

Question 2: x_{n+1}= {\Large \frac {x_n+14}{2}}, \qquad x_0=6 |

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

Question 4: u_{n+1}= {\Large \frac {u_n}{u_n-1}}, \qquad u_0=9 |

Question 5: x_{n+1}=x_n^2+4x_n-10, \qquad x_0=2 |

Question 6: Show that the equation x^2-3x-1=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

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

Question 8: Show that the equation x^2+11x-11=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 9: Show that the equation x^2-9x-17=0 has a solution between \ x=10\ \textrm{and} \ x=11 |

Question 10: Show that the equation x^2-7x-7=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

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# Answers

Question 1: u_{1}=-1,\qquad u_{2}=-5,\qquad u_{3}=-13,\qquad u_{4}=-29,\qquad u_{5}=-61 |

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

Question 3: a_{1}=14,\qquad a_{2}=47,\qquad a_{3}=146,\qquad a_{4}=443,\qquad a_{5}=1334 |

Question 4: u_{1}={\Large \frac {9}{8}},\qquad u_{2}=9,\qquad u_{3}={\Large \frac {9}{8}},\qquad u_{4}=9,\qquad u_{5}={\Large \frac {9}{8}} |

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

Question 6: f(-1)=3 > 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 7: f(-3)=1 > 0, f(-2)=-2 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-3\ \textrm{and} \ x=-2 |

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

Question 9: f(10)=-7 < 0, f(11)=5 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=10\ \textrm{and} \ x=11 |

Question 10: f(-1)=1 > 0, f(0)=-7 < 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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