Hello, Bowier4!
Sorry, your answer is wrong . . .
You answered the wrong question anyway (the number in the tenth row).
For a bulletin-board display, Laurie is putting one pictures in the first row,
3 in the second row,6 in the third row,and 10 in the fourth row.
If the pattern continues, how many pictures will she need for ten rows?
TchrWill is absolutely correct!
The numbers are called "Triangular Numbers" for rather obvious reasons:
Code:
o
o o o
o o o o o o
o o o o o o o o o o
o o o o o o o o o o o o o o o
1 3 6 10 15
TW also gave us the formula for the n<sup>th</sup> triangular number: \(\displaystyle \,T_n\:=\:\frac{n(n\,+\,1)}{2}\)
The sum of the first \(\displaystyle n\) triangular numbers is: \(\displaystyle \,S_n\;=\;\frac{n(n\,+\,1)(n\,+\,2)}{6}\)
I played with this concept years ago and called these new numbers
tetrahedral.
\(\displaystyle \;\;\)If you "stack" the triangular numbers, you get a triangular pyramid, a tetrahedron.
To answer the question, the sum of the first 10 triangular number is:
\(\displaystyle \;\;\;S_{10}\;=\;\frac{(10)(11)(12)}{6}\;=\;220\)
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And now you can answer the question:
How many gifts did my true love give to me during The Twelve Days of Christmas?
