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Question 1: The first 2 terms of a linear sequence are: 6a and 4b a) Show that the 5th term is 16b - 18a b) Given that the 3rd term is 18 and the 5th term is 6, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 5a and 2b a) Show that the 6th term is 10b - 20a b) Given that the 4th term is -132 and the 6th term is -250, 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 -33 and the 4th term is -59 , calculate a and b. |

Question 4: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn - 6. Given that the 4th term is -150 and the 5th term is -221 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 3a and 4b a) Show that the 7th term is 15a + 32b b) Given that the 4th term is -54 and the 7th term is -198, 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 -216 and the 3rd term is -36, calculate a and b. |

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Question 1: a) A linear sequence has the same difference, d, between each term. d = 4b - 6a => 3rd term is 4b + d and the 5th term is 4b + 3d b) a = 5, b = 6 |

Question 2: a) A linear sequence has the same difference, d, between each term. d = 2b - 5a => 3rd term is 2b + d and the 6th term is 2b + 4d b) a = 9, b = -7 |

Question 3: a = -3, b = -5 |

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