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

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

Question 2: a_{n+1}= {\Large \frac {a_n+16}{2}}, \qquad a_0=6 |

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

Question 4: u_{n+1}=25-u_n, \qquad u_0=27 |

Question 5: a_{n+1}=a_n^2-6a_n+10, \qquad a_0=5 |

Question 6: Show that the equation x^2+7x-19=0 has a solution between \ x=-10\ \textrm{and} \ x=-9 |

Question 7: Show that the equation x^2+8x-13=0 has a solution between \ x=-10\ \textrm{and} \ x=-9 |

Question 8: Show that the equation x^2-4x-3=0 has a solution between \ x=4\ \textrm{and} \ x=5 |

Question 9: Show that the equation x^2+8x-5=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

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

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# Answers

Question 1: u_{1}=7,\qquad u_{2}=19,\qquad u_{3}=67,\qquad u_{4}=259,\qquad u_{5}=1027 |

Question 2: a_{1}=11,\qquad a_{2}=13.5,\qquad a_{3}=14.75,\qquad a_{4}=15.375,\qquad a_{5}=15.6875 |

Question 3: x_{1}=7,\qquad x_{2}=19,\qquad x_{3}=43,\qquad x_{4}=91,\qquad x_{5}=187 |

Question 4: u_{1}=-2,\qquad u_{2}=27,\qquad u_{3}=-2,\qquad u_{4}=27,\qquad u_{5}=-2 |

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

Question 6: f(-10)=11 > 0, f(-9)=-1 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-10\ \textrm{and} \ x=-9 |

Question 7: f(-10)=7 > 0, f(-9)=-4 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-10\ \textrm{and} \ x=-9 |

Question 8: f(4)=-3 < 0, f(5)=2 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=4\ \textrm{and} \ x=5 |

Question 9: 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 10: f(2)=-2 < 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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