Name: Date:

Question 1: The first 2 terms of a linear sequence are: 8a and 5b a) Show that the 5th term is 20b - 24a b) Given that the 3rd term is -78 and the 5th term is -204, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 7a and 3b a) Show that the 6th term is 15b - 28a b) Given that the 4th term is -76 and the 6th term is -164, calculate a and b. |

Question 3: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn + 8. Given that the 3rd term is -85 and the 4th term is -148 , calculate a and b. |

Question 4: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn - 2. Given that the 3rd term is 52 and the 5th term is 158 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 2a and 8b a) Show that the 7th term is 10a + 64b b) Given that the 6th term is 224 and the 7th term is 360, calculate a and b. |

Question 6: The first 2 terms of a geomtric sequence are: -2a and -2a \sqrt {5b} a) Show that the 5th term is -50ab^2 b) Given that the 5th term is -3,600 and the 3rd term is -120, calculate a and b. |

Show Answers
Hide Answers

© GCSEMathsWorksheets.com

# Answers

Question 1: a) A linear sequence has the same difference, d, between each term. d = 5b - 8a => 3rd term is 5b + d and the 5th term is 5b + 3d b) a = 6, b = -3 |

Question 2: a) A linear sequence has the same difference, d, between each term. d = 3b - 7a => 3rd term is 3b + d and the 6th term is 3b + 4d b) a = 8, b = 4 |

Question 3: a = -8, b = -7 |

Question 4: a = 7, b = -3 |

Question 5: a) The next term in a Fibonacci sequence is calculated by adding the 2 previous terms, so the 3rd term = 2a + 8b etc. b) a = 4, b = 5 |

Question 6: a) The next term in a geometric sequence is calculated by multiplying the current term by the same common ratio ,r = {\Large \frac {-2a \sqrt {5b}}{-2a}} = \sqrt {5b} so the 3rd term = -10ab etc. b) a = 2, b = 6 |