Arithmetic Sequences with a common difference may be defined by a first order difference equation.
An arithmetic sequence where there is a common difference of can be defined by a first order difference equation of the form:
Where is the common difference
is an increasing sequence
is a decreasing sequence
A difference equation must have a common difference and no common ratio for it to define an arithmetic sequence.
Determine whether each of the following first order difference equations defines and arithmetic sequence.
The first order difference equation defines a decreasing arithmetic sequence with a common difference of -7.
The first order difference equation defines an increasing arithmetic sequence with a common difference of 5.
The first order difference equation does not define an arithmetic sequence as the term has a coefficient of 3.
An arithmetic sequence can be expressed as a first order difference equation by finding the initial or starting term and the common difference. This is then substituted into the general equation above.
Express each of the following arithmetic sequences as first order difference equations.
First we must check for a common difference.
We know that the first term is -22 and the common difference is 7 so we can now put these into the equation.
Again, we must check for a common difference.
We know that the first term is 23 and the common difference is -5 so we can now put these into the equation.
Want to suggest an edit? Have some questions? General comments? Let us know how we can make this resource more useful to you.