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Question 1: The first 2 terms of a linear sequence are: 2a and 9b a) Show that the 5th term is 36b - 6a b) Given that the 3rd term is -96 and the 5th term is -198, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 4a and 5b a) Show that the 6th term is 25b - 16a b) Given that the 4th term is 19 and the 6th term is 13, 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 52 and the 5th term is 132 , 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 100 and the 4th term is 170 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 7a and 8b a) Show that the 7th term is 35a + 64b b) Given that the 4th term is -109 and the 7th term is -401, calculate a and b. |

Question 6: The first 2 terms of a geomtric sequence are: -4a and -4a \sqrt {5b} a) Show that the 5th term is -100ab^2 b) Given that the 5th term is 4,500 and the 3rd term is 300, calculate a and b. |

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Question 1: a) A linear sequence has the same difference, d, between each term. d = 9b - 2a => 3rd term is 9b + d and the 5th term is 9b + 3d b) a = 3, b = -5 |

Question 2: a) A linear sequence has the same difference, d, between each term. d = 5b - 4a => 3rd term is 5b + d and the 6th term is 5b + 4d b) a = 7, b = 5 |

Question 3: a = 4, b = 8 |

Question 4: a = 9, b = 7 |

Question 5: a) The next term in a Fibonacci sequence is calculated by adding the 2 previous terms, so the 3rd term = 7a + 8b etc. b) a = 5, b = -9 |

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 {-4a \sqrt {5b}}{-4a}} = \sqrt {5b} so the 3rd term = -20ab etc. b) a = -5, b = 3 |