Number Sequences


In these lessons, we will look at various types of number sequences and how to solve problems related to number sequences.

In another set of lessons, we have some examples of Integer Word Problems that involve two unknowns.




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Related Pages
Linear Sequences
Geometric Sequences
Quadratic and Cubic Sequences

The following diagrams give the formulas for Arithmetic Sequence and Geometric Sequence. Scroll down the page for examples and solutions.
Arithmetic Sequence

Geometric Sequence

How To Find The Next Term In A Number Sequence?

A number sequence is a list of numbers arranged in a row. Let us look at two examples below.
(i) 4, 6, 1, 10, 14, 5, …
(ii) 4, 7, 10, 13, ….

Number sequence (i) is a list of numbers without order or pattern. You cannot tell what number comes after 5.

Number sequence (ii) has a pattern. Do you observe that each number is obtained by adding 3 to the preceding number (i.e. the number just before it)?

In these lesson, we will only study number sequences with patterns.

Some other examples of number sequences are:

Number Sequence Pattern
3, 6, 9, 12, ... add 3
12, 17, 22, 27, ... add 5
70, 65, 60, 55, ... subtract 5
15, 19, 23, 27, … add 4
81, 27, 9, 3, … divide by 3



How To Complete Missing Terms In A Number Sequence?

Each of the number in the sequence is called a term. In order to find the missing terms in a number sequence, we must first find the pattern of the number sequence.

Example:
Find the missing terms in the following sequence:
8, ______, 16, ______, 24, 28, 32

Solution:
To find the pattern, look closely at 24, 28 and 32. Each term in the number sequence is formed by adding 4 to the preceding number. So, the missing terms are 8 + 4 = 12 and 16 + 4 = 20. Check that the pattern is correct for the whole sequence from 8 to 32.

Example:
What is the value of n in the following number sequence?

16, 21, n, 31, 36

Solution:
We find that the number pattern of the sequence is “add 5” to the preceding number.
So, n = 21 + 5 = 26

How To Find The Next Term In A Number Sequence?

The following video shows some examples of how to determine the next term in a number sequence.

Examples:
Find the next number

  1. 1, 8, 15, 22, …
  2. 1, 8, 64, 512, …
  3. 1, 8, 27, 64, …
  4. 1, 8, 16, 15, …

How To Find The nth Term Of An Arithmetic Sequence

Example:
7, 9, 11, 13, 15, …

How To Find The nth Term Of A Geometric Sequence

Example:
5, 10, 20, 40, …



Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget



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