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

Question 1: x_{n+1}=3x_n-5, \qquad x_0=8 |

Question 2: u_{n+1}= {\Large \frac {u_n+10}{2}}, \qquad u_0=8 |

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

Question 4: x_{n+1}= {\Large \frac {x_n}{x_n-1}}, \qquad x_0=8 |

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

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

Question 7: Show that the equation x^2+10x-7=0 has a solution between \ x=-11\ \textrm{and} \ x=-10 |

Question 8: Show that the equation x^2-6x-17=0 has a solution between \ x=8\ \textrm{and} \ x=9 |

Question 9: Show that the equation x^2-5x-11=0 has a solution between \ x=6\ \textrm{and} \ x=7 |

Question 10: Show that the equation x^2+7x-19=0 has a solution between \ x=2\ \textrm{and} \ x=3 |

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# Answers

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

Question 2: u_{1}=9,\qquad u_{2}=9.5,\qquad u_{3}=9.75,\qquad u_{4}=9.875,\qquad u_{5}=9.9375 |

Question 3: a_{1}=13,\qquad a_{2}=43,\qquad a_{3}=133,\qquad a_{4}=403,\qquad a_{5}=1213 |

Question 4: x_{1}={\Large \frac {8}{7}},\qquad x_{2}=8,\qquad x_{3}={\Large \frac {8}{7}},\qquad x_{4}=8,\qquad x_{5}={\Large \frac {8}{7}} |

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

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

Question 7: f(-11)=4 > 0, f(-10)=-7 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-11\ \textrm{and} \ x=-10 |

Question 8: f(8)=-1 < 0, f(9)=10 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=8\ \textrm{and} \ x=9 |

Question 9: f(6)=-5 < 0, f(7)=3 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=6\ \textrm{and} \ x=7 |

Question 10: f(2)=-1 < 0, f(3)=11 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=2\ \textrm{and} \ x=3 |

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