How many cubes are in the 10th collection of cubes in this sequence?

1st- 1 cube

2nd- 4 cubes

3rd- 10 cubes.....

l

l

l

10th- ? cubes

Any help appreciated!

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- March 23rd 2009, 11:36 AMphillyfan09Elementary Math Problem
How many cubes are in the 10th collection of cubes in this sequence?

1st- 1 cube

2nd- 4 cubes

3rd- 10 cubes.....

l

l

l

10th- ? cubes

Any help appreciated! - March 23rd 2009, 12:38 PMGrandadTetrahedral numbers
Hello phillyfan09The sequence 1, 4, 10, ... is sometimes called Tetrahedral Numbers. Here's the answer to your question: Tetrahedral number - Wikipedia, the free encyclopedia.

Grandad - March 23rd 2009, 05:04 PMSoroban
Hello, phillyfan09!

Where did this problem come from?

It doesn't give enough information to allow us a good guess.

Lucky for us, Grandad recognized the sequence.

Quote:

How many cubes are in the 10th collection of cubes in this sequence?

. .

Imagine a display of oranges, stacked in a triangular pyramid (tetrahedron).

. . Each horizontal level is an equilateral triangle.

And we want the 10th Total on this list.

You can crank out the numbers yourself, or you can use this formula:

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

By the way, this formula answers the question:

How many gifts did My True Love Give To Me

. . during the Twelve Days of Christmas?

. .

- March 24th 2009, 07:16 AMphillyfan09
Problem came from a college level elementary course...I believe professor made it up.

Thanks!