Number patterns

# Number patterns

#### Question 1

Look at this number sequence. | |

2, 6, 18, 54 | |

The rule for this number sequence is: | |

a |
start with 2 and multiply by 3 each time. |

b |
start with 2 and multiply by 4 each time. |

c |
start with 2, double and add 2 each time. |

d |
start with 2, multiply by 4 and subtract 2 each time. |

#### Solution

This question is multiple-choice and so we know that the answer is one of the four given.

There are four terms in this sequence.

Term 1: 2

Term 2: 6

Term 3: 18

Term 4: 54

Term 1 is 2. We multiply by 3 to get 6 (Term 2). We multiply 6 by 3 to get 18 (Term 3). We multiply 18 by 3 to get 54 (Term 4).

We have:

2 × 3 = 6. | 6 × 3 = 18. | 18 × 3 = 54. |

The answer is the first given.

We can check that the other alternatives do not work but this is not necessary as only one correct answer is given in multiple-choice questions.

For the second alternative the terms are:

Term 1: 2 | Term 2: 8 | Term 3: 32 | Term 4: 128 |

For the third alternative the terms are:

Term 1: 2 | Term 2: 6 | Term 3: 14 | Term 4: 30 |

For the fourth alternative the terms are:

Term 1: 2 | Term 2: 6 | Term 3: 22 | Term 4: 86 |

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