I just covered arithmetic sequences and how to develop algebraic rule for the pattern to prepare my 7th graders for their state test. The next question they faced was similar, but it wasn't an arithmetic sequence.

The pattern was:

1

5

14

30

55

....etc

So you are adding:

2^2

then 3^2

then 4^2

There was a nice picture of a pyramid of cans so you could see the new cans represented by 2 squared, and 3 squared. I assume because there is a pattern, there has to be an algebraic rule to finding the number of cans of the nth term but am unsure what it is.

I know the new cans are n squared and you add them to the total number of cans from the previous term, but am not sure how to represent that in an equation.

Is it really complicated, am I just not seeing it? Help!