Number Series Practice and Tutorials


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

Number Series Tutorial

Number Sequences (Algebraic)

See also number sequence (Algebra)

Strategy for Answering Number Series     Practice Questions     Answer Key

 

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:
Modified: August 22nd, 2018 August 22nd, 2018

Published: May 12th, 2014

3 thoughts on “Number Series Practice and Tutorials”

    1. 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.

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