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

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

Question 2: u_{n+1}= {\Large \frac {u_n+14}{2}}, \qquad u_0=12 |

Question 3: a_{n+1}=2a_n+4, \qquad a_0=3 |

Question 4: x_{n+1}=40-x_n, \qquad x_0=10 |

Question 5: u_{n+1}=u_n^2-2u_n-4, \qquad u_0=4 |

Question 6: Show that the equation x^2+4x-7=0 has a solution between \ x=1\ \textrm{and} \ x=2 |

Question 7: Show that the equation x^2+8x-23=0 has a solution between \ x=-11\ \textrm{and} \ x=-10 |

Question 8: Show that the equation x^2+2x-13=0 has a solution between \ x=-5\ \textrm{and} \ x=-4 |

Question 9: Show that the equation x^2+5x-1=0 has a solution between \ x=-6\ \textrm{and} \ x=-5 |

Question 10: Show that the equation x^2+3x-17=0 has a solution between \ x=-6\ \textrm{and} \ x=-5 |

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# Answers

Question 1: x_{1}=18,\qquad x_{2}=70,\qquad x_{3}=278,\qquad x_{4}=1110,\qquad x_{5}=4438 |

Question 2: u_{1}=13,\qquad u_{2}=13.5,\qquad u_{3}=13.75,\qquad u_{4}=13.875,\qquad u_{5}=13.9375 |

Question 3: a_{1}=10,\qquad a_{2}=24,\qquad a_{3}=52,\qquad a_{4}=108,\qquad a_{5}=220 |

Question 4: x_{1}=30,\qquad x_{2}=10,\qquad x_{3}=30,\qquad x_{4}=10,\qquad x_{5}=30 |

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

Question 6: f(1)=-2 < 0, f(2)=5 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=1\ \textrm{and} \ x=2 |

Question 7: f(-11)=10 > 0, f(-10)=-3 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-11\ \textrm{and} \ x=-10 |

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

Question 9: f(-6)=5 > 0, f(-5)=-1 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-6\ \textrm{and} \ x=-5 |

Question 10: 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 |

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