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Question 1: The first 2 terms of a linear sequence are: 4a and 8b a) Show that the 5th term is 32b - 12a b) Given that the 3rd term is -48 and the 5th term is -64, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 9a and 2b a) Show that the 6th term is 10b - 36a b) Given that the 4th term is 96 and the 6th term is 184, calculate a and b. |

Question 3: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn - 7. Given that the 4th term is 145 and the 5th term is 228 , calculate a and b. |

Question 4: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn + 4. Given that the 3rd term is 43 and the 5th term is 139 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 6a and 4b a) Show that the 7th term is 30a + 32b b) Given that the 4th term is -52 and the 7th term is -220, calculate a and b. |

Question 6: The first 2 terms of a geomtric sequence are: 5a and 5a \sqrt {2b} a) Show that the 5th term is 20ab^2 b) Given that the 5th term is -4,320 and the 3rd term is -360, calculate a and b. |

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Question 1: a) A linear sequence has the same difference, d, between each term. d = 8b - 4a => 3rd term is 8b + d and the 5th term is 8b + 3d b) a = -8, b = -5 |

Question 2: a) A linear sequence has the same difference, d, between each term. d = 2b - 9a => 3rd term is 2b + d and the 6th term is 2b + 4d b) a = -4, b = 4 |

Question 3: a = 9, b = 2 |

Question 4: a = 7, b = -8 |

Question 5: a) The next term in a Fibonacci sequence is calculated by adding the 2 previous terms, so the 3rd term = 6a + 4b etc. b) a = -2, 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 {5a \sqrt {2b}}{5a}} = \sqrt {2b} so the 3rd term = 10ab etc. b) a = -6, b = 6 |