Continue these sequences. Explain how each one works.

a. | 0 | 1 | 3 | 6 | 7 | 9 | 12 | 13 | ___ | ___ | ___ |

b. | 1 | 2 | 3 | 4 | 9 | 8 | 27 | 16 | ___ | ___ | ___ |

c. | 0 | 4 | 8 | 4 | 8 | 12 | 6 | 10 | ___ | ___ | ___ |

d. | 1 | 2 | 3 | 3 | 6 | 9 | 9 | ___ | ___ | ___ | ___ |

e. | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | ___ | ___ | ___ |

f. | 0 | 1 | 1 | 2 | 4 | 7 | 13 | 24 | ___ | ___ | ___ |

Here are some possible solutions. You may well find others that work.

a. | 0 | 1 | 3 | 6 | 7 | 9 | 12 | 13 | 15 | 18 | 19 | |

Successive differences are 1,2,3 repeated. | ||||||||||||

b. | 1 | 2 | 3 | 4 | 9 | 8 | 27 | 16 | 81 | 32 | 243 | |

Terms are successive powers of 2 and 3. | ||||||||||||

c. | 0 | 4 | 8 | 4 | 8 | 12 | 6 | 10 | 14 | 8 | 12 | |

Starting with 4, successive even numbers are added to 0,4,8. | ||||||||||||

d. | 1 | 2 | 3 | 3 | 6 | 9 | 9 | 18 | 27 | 27 | 54 | |

The terms 1,2,3 are multipled by successive powers of 3. | ||||||||||||

e. | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | |

Regular ol’ Fibonacci sequence. | ||||||||||||

f. | 0 | 1 | 1 | 2 | 4 | 7 | 13 | 24 | 44 | 81 | 149 | |

Starting with the fourth term, each term is the sum of the preceding three terms. Super-Fibonacci, anyone? |