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Question 1: The first 2 terms of a linear sequence are: 6a and 7b a) Show that the 5th term is 28b - 18a b) Given that the 3rd term is -46 and the 5th term is -110, calculate a and b. |

Question 2: The first 2 terms of a linear sequence are: 3a and 4b a) Show that the 6th term is 20b - 12a b) Given that the 4th term is 138 and the 6th term is 240, calculate a and b. |

Question 3: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn + 3. Given that the 3rd term is -30 and the 4th term is -65 , calculate a and b. |

Question 4: The n^{th} term of a quadratic sequence is of the form: an^{2} + bn - 9. Given that the 3rd term is -102 and the 5th term is -244 , calculate a and b. |

Question 5: The first 2 terms of a Fibonacci sequence are: 9a and 3b a) Show that the 6th term is 27a + 15b b) Given that the 5th term is -54 and the 6th term is -75, 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 2,880 and the 3rd term is 240, calculate a and b. |

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Question 1: a) A linear sequence has the same difference, d, between each term. d = 7b - 6a => 3rd term is 7b + d and the 5th term is 7b + 3d b) a = 3, b = -2 |

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

Question 3: a = -6, b = 7 |

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

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

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 = 5, b = 6 |