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