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Question 1: The first 2 terms of a linear sequence are: 3a and 4b a) Show that the 5th term is 16b - 9a b) Given that the 3rd term is 67 and the 5th term is 161, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 8a and 2b a) Show that the 6th term is 10b - 32a b) Given that the 4th term is 6 and the 6th term is -6, calculate a and b. |

Question 3: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn + 9. Given that the 3rd term is 57 and the 4th term is 85 , 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 4th term is -63 and the 5th term is -87 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 7a and 6b a) Show that the 7th term is 35a + 48b b) Given that the 5th term is -76 and the 7th term is -184, calculate a and b. |

Question 6: The first 2 terms of a geomtric sequence are: 3a and 3a \sqrt {2b} a) Show that the 5th term is 12ab^2 b) Given that the 5th term is -900 and the 3rd term is -90, calculate a and b. |

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

Question 2: a) A linear sequence has the same difference, d, between each term. d = 2b - 8a => 3rd term is 2b + d and the 6th term is 2b + 4d b) a = 3, b = 9 |

Question 3: a = 3, b = 7 |

Question 4: a = -2, b = -6 |

Question 5: a) The next term in a Fibonacci sequence is calculated by adding the 2 previous terms, so the 3rd term = 7a + 6b etc. b) a = -8, b = 2 |

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 {3a \sqrt {2b}}{3a}} = \sqrt {2b} so the 3rd term = 6ab etc. b) a = -3, b = 5 |