Find the nth term of figurative number

Question

The nth square number , Sn, equals the sum of the first n odd natural numbers. The nth value of what figurative number equals the sum of the first n even natural numbers? To put it another way, 2+4+6+...+2n= the nth term of what figurative number?

 

This is my work:

 

2+4+6+...+2n-6+2n-4+2n-2

2n-2+2n-4+2n-6+...+2+4+6

 

2n+2n+2n...2n+2n+2n

 

n sets of 2n= n(2n)= 2n^2/2= n^2

The nth

Answer 1

I believe the figure that gives this sequence is a parallelogram where the length is one more than the width.

 

To see this, start by putting two blocks next to each other.  That is a 1x2 rectangle.  Then add another row of blocks around the figure -- along the top and around the side.  That adds 4 blocks.  Repeat the procedure and you add 6 blocks.  Etc.

 

Though it's easiest to see the pattern if the figure is rectangular, it does not have to be.  The same pattern results from a parallelogram.