Nora M.

asked • 06/01/15# Find the nth term of figurative number

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

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## 1 Expert Answer

Jon P. answered • 06/02/15

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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.

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Mark M.

06/01/15