We can generate the terms of a sequence by using the rule for first order difference equations.
A reminder of what a general first order difference equation looks like:
Find the first four terms of the sequence defined by the first order difference equation:
We know that the starting term () so we can generate the next term () by completing the equation.
Now use to calculate
Now use to find
The first four terms are 8, 20, 44 and 92.
A sequence is defined by the first order difference equation:
If , what is the third term?
We need to calculate the previous term so transpose the equation to make the subject.
Now, use to find using the transposed equation.
Now we can use to find .
The third term is 78.
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