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

Question 2