Patterns and variables

For a given pattern (1,4,9,16..)

What is the value for the nth number in the series and what is the pattern?

We have a difference in opinion with my son's 5th grade math teacher and want to get consensus.

• Just out of curiosity, what is the difference of opinion? This seems obviously to be the list of perfect squares. – lulu Dec 2 '17 at 14:32
• The teacher was using the recursive way referenced below to represent the sequence and given that we were struggling to get to the nth number. Using the list of perfect squares the answer was obvious. – Math Monkey Dec 2 '17 at 14:57
• Ah. Of course, those two expressions describe the same sequence. Worth noting that not all recursively defined sequences have pleasant closed formulas, so it is worth seeing both approaches. – lulu Dec 2 '17 at 15:22

This is the following succession: $$a_n=n^2$$.
$$a_1=1$$
$$a_n=a_{n-1}+(2n-1)$$