We can recognize the sequence is an arithmetic progression by noticing that the common difference between each term is 6.

where f(n) is the sequence

n is the term number

d is the common difference

and a is the starting term

where f(n) is the sequence

n is the term number

d is the common difference

and a is the starting term

We are well aware that our starting term, and hence a, is 2 and our difference, and hence d, is 6.

So our polynomial function is