# Number Series Practice and Tutorials

- Posted by Brian Stocker MA
- Date Published May 12, 2014
- Date modified April 3, 2019
- Comments 4 comments

Number series are where a series of numbers are given and students must calculate either the missing numbers or the number that follows.

Standardized Tests such as the Ontario Police, Canadian Armed Forces Entrance Test, COOP, HSPT

See also number sequence (Algebra)

### Strategy for Answering Number Series Questions

Here is a quick method that will help you answer number

series.

For example:

2, 5, 6, 7, 8,

**Step 1** – glance at the series quickly and see if you can spot the pattern right away. First look for obvious differences – 2X, 5X, 1/2, 1/4 etc.

**Step 2** – Start analyzing. If you can’t find an obvious answer, get to work.

Take the different between the first 2 numbers and the different between the second 2 numbers.

2, (+3) 5, (+1) 6, (+1) 7, (+1) 8,

No clear pattern with a simple analysis. There is no addition,

subtraction, multiplication, division, fractional or exponent

relationship.

The relation must be a higher order or a second series.

Next look at the relation between the 1st number and the

2nd and the 1st and the 3rd. We see that,

1st + 3 = 5, 1st + 4 = 6. That’s it! The number 2 is added

to the sequence, 3, 4, 5, 6, so the next number will be 2 +

7 = 9.

### Practice Questions

**1. Consider the following series: 6, 12, 24, 48. What number should ****come next?**

a. 48

b. 64

c. 60

d. 96

**2. Consider the following series: 5, 6, 11, 17. What number should ****come next?**

a. 28

b. 34

c. 36

d. 27

**3. Consider the following series: 26, 21, …, 11, 6. What is the missing ****number?**

a. 27

b. 23

c. 16

d. 29

**4. Consider the following series:23, …, 31, 37. What is the missing ****number?**

a. 19

b. 27

c. 29

d. 30

**5. Consider the following series: 3, 6, 11, 18. What number should ****come next?**

a. 30

b. 27

c. 22

d. 29

**6. Consider the following series: 26, 24, 20, 14. What number should ****come next?**

a. 6

b. 18

c. 12

d. 8

**7. Consider the following series: 6, 8, 4, 10, 18, 22. What number ****should come next?**

a. 34

b. 32

c. 24

d. 26

**8. Consider the following series: L, O, R, …, X. What is the missing ****letter?**

a. S

b. U

c. T

d. M

**9. Consider the following series: X, Z, B, D. What letter should ****come next? **

a. E

b. F

c. G

d. H

**10. Consider the following series: 25, 33, 41, 49. What number ****should come next?**

a. 51

b. 55

c. 59

d. 57

### Answer Key

**1. D**

The numbers double each time.

**2. A**

Each number is the sum of the previous two numbers.

**3. C**

The numbers decrease by 5 each time.

**4. C**

The numbers are primes (divisible only by 1 and themselves).

**5. B**

The interval, beginning with 3, increases by 2 each time.

**6. A**

The interval, beginning with 2, increases by 2, and is subtracted each time.

**7. B**

Each number is the sum of the previous and the number 2 places to the

left.

**8. B**

There are two letters missing between each one, so U is next.

**9. B**

Miss a letter each time and ‘loop’ back, so F is next.

**10. D**

The numbers increase by 8.

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

## 4 Comments

thank you (:

Are you open to explaining #7 a bit more? I am a bit confused by it. Thanks.

Here is the sequence 6, 8, 4, 10, 18, 22.

so – it is the sum of the number and the number 2 spaces back. Starting at 4 as we don’t know the number before 6, 6 + 4 = 10, then 8 + 10 = 18, and 22 + 10 = 32.

For number 4 I would say there is an alternate answer.

By assuming that the second number in the sequence is 27 (b) you can create a pattern in which the 3rd number is +8 bigger than the 1st, 4th is +10 bigger that the 2nd, and hypothetically the 5th number (43) is +12 bigger than the 3rd.

Just thought it was interesting.