The function below models the number of bonus points earned for completing the nth level of a certain video game. f(n)=2,000+750n , where n=1,  2,  3,   which sequence does the function f(n) generate?

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.