To check what kid of sequence the function
generates, we are going to evaluate the function at
,
, and
to find the first three terms of our sequence. Then, we are going to check if the sequence has a constant difference,
, which means the sequence will be arithmetic, or a constant ratio
, which means the sequence will be geometric.
So, we have the sequence 2750,3500,4250,... Lets find if it has a constant difference. To do that we are going to use the formula
; in other words we are going subtract the current number from the previous one:
Notice that the difference,
, is constant, so we have a arithmetic sequence.
We can conclude that the sequence the function
generates is an
arithmetic sequence.
