Introduction
An arithmetic sequence is a list of numbers where each term increases or decreases by the same fixed amount, called the common difference.
For example:
Here, the common difference is 3.
The nth term of an arithmetic sequence is given by:
where 
is the first term and d is the common difference.
The sum of the first n terms is:
Example
The 3rd term of an arithmetic sequence is 10, and the 7th term is 22. Find the first term and the common difference.
Solution:
Subtracting the first from the second:
Substitute back:
So the sequence is:
Practice Questions & Solutions
The fourth term of an arithmetic sequence is 14 and the sixth term is 20. Determine the sequence.
Subtract:
Then:
Sequence:
The first term of an arithmetic sequence is 3 and the fifteenth term is 45. Find the common difference and the sum of the first fifteen terms.
Sum of the first 15 terms:
Common difference:
Sum:
Find the sum of the first fifteen multiples of 7.
Sum:
Find the sum of the first fifteen numbers ending in 5.
Sum:
Find the sum of the first fifteen even numbers greater than 20.
Sum:
Find the angles of a convex quadrilateral, knowing they are in arithmetic sequence and their sum is 360 degrees.
Let the angles be:
If 
and 
, then the angles are:
The shorter leg of a right triangle is 6cm. The sides form an arithmetic sequence. Find the lengths of the other two sides.
Let the sides be:
Given 
:
Solve for d:
Reject the negative value.
Sides:
Find three numbers in an arithmetic sequence whose sum is 15 and the sum of their squares is 83.
Let the numbers be:
Numbers:
Did you like this article? Rate it!
Loading...