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

Question 1: u_{n+1}=2u_n-4, \qquad u_0=7 |

Question 2: a_{n+1}= {\Large \frac {a_n+14}{2}}, \qquad a_0=8 |

Question 3: x_{n+1}=4x_n+2, \qquad x_0=4 |

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

Question 5: a_{n+1}=a_n^2-3a_n+3, \qquad a_0=3 |

Question 6: Show that the equation x^2-7x-3=0 has a solution between \ x=-1\ \textrm{and} \ x=0 |

Question 7: Show that the equation x^2-10x-19=0 has a solution between \ x=11\ \textrm{and} \ x=12 |

Question 8: Show that the equation x^2+8x-5=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 9: Show that the equation x^2-12x-2=0 has a solution between \ x=12\ \textrm{and} \ x=13 |

Question 10: Show that the equation x^2+5x-23=0 has a solution between \ x=2\ \textrm{and} \ x=3 |

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# Answers

Question 1: u_{1}=10,\qquad u_{2}=16,\qquad u_{3}=28,\qquad u_{4}=52,\qquad u_{5}=100 |

Question 2: a_{1}=11,\qquad a_{2}=12.5,\qquad a_{3}=13.25,\qquad a_{4}=13.625,\qquad a_{5}=13.8125 |

Question 3: x_{1}=18,\qquad x_{2}=74,\qquad x_{3}=298,\qquad x_{4}=1194,\qquad x_{5}=4778 |

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

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

Question 6: f(-1)=5 > 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 7: 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 8: f(0)=-5 < 0, f(1)=4 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

Question 9: f(12)=-2 < 0, f(13)=11 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=12\ \textrm{and} \ x=13 |

Question 10: f(2)=-9 < 0, f(3)=1 > 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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