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Question 1: The first 2 terms of a linear sequence are: 4a and 9b a) Show that the 5th term is 36b - 12a b) Given that the 3rd term is -108 and the 5th term is -180, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 7a and 2b a) Show that the 6th term is 10b - 28a b) Given that the 4th term is 84 and the 6th term is 154, 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 4th term is -64 and the 5th term is -102 , calculate a and b. |

Question 4: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn + 7. Given that the 3rd term is 1 and the 5th term is 17 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 7a and 4b a) Show that the 6th term is 21a + 20b b) Given that the 5th term is 90 and the 6th term is 129, calculate a and b. |

Question 6: The first 2 terms of a geomtric sequence are: -4a and -4a \sqrt {2b} a) Show that the 5th term is -16ab^2 b) Given that the 5th term is 5,184 and the 3rd term is 432, calculate a and b. |

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Question 1: a) A linear sequence has the same difference, d, between each term. d = 9b - 4a => 3rd term is 9b + d and the 5th term is 9b + 3d b) a = -9, b = -8 |

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

Question 3: a = -4, b = -2 |

Question 4: a = 2, b = -8 |

Question 5: a) The next term in a Fibonacci sequence is calculated by adding the 2 previous terms, so the 3rd term = 7a + 4b etc. b) a = 9, b = -3 |

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 {2b}}{-4a}} = \sqrt {2b} so the 3rd term = -8ab etc. b) a = -9, b = 6 |