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

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

Question 2: a_{n+1}= {\Large \frac {a_n+12}{2}}, \qquad a_0=18 |

Question 3: u_{n+1}=2u_n+4, \qquad u_0=3 |

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

Question 5: a_{n+1}=a_n^2-7a_n+11, \qquad a_0=5 |

Question 6: Show that the equation x^2-7x-23=0 has a solution between \ x=9\ \textrm{and} \ x=10 |

Question 7: Show that the equation x^2+9x-1=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 8: Show that the equation x^2+20x-11=0 has a solution between \ x=0\ \textrm{and} \ x=1 |

Question 9: Show that the equation x^2-9x-19=0 has a solution between \ x=-2\ \textrm{and} \ x=-1 |

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

Show Answers
Hide Answers

© GCSEMathsWorksheets.com

# Answers

Question 1: x_{1}=13,\qquad x_{2}=49,\qquad x_{3}=193,\qquad x_{4}=769,\qquad x_{5}=3073 |

Question 2: a_{1}=15,\qquad a_{2}=13.5,\qquad a_{3}=12.75,\qquad a_{4}=12.375,\qquad a_{5}=12.1875 |

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

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

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

Question 6: f(9)=-5 < 0, f(10)=7 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=9\ \textrm{and} \ x=10 |

Question 7: f(0)=-1 < 0, f(1)=9 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

Question 8: f(0)=-11 < 0, f(1)=10 > 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=0\ \textrm{and} \ x=1 |

Question 9: f(-2)=3 > 0, f(-1)=-9 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-2\ \textrm{and} \ x=-1 |

Question 10: f(-9)=5 > 0, f(-8)=-5 < 0 \textrm{there is a change of sign} \implies \textrm{there is a solution between} \ x=-9\ \textrm{and} \ x=-8 |

© GCSEMathsWorksheets.com