SOLUTION: Carmen is playing with blocks. She arranges stacks of blocks so that each successive level of blocks has 1 fewer block than the level below it and the top level has 1 block. The l

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Question 1090413: Carmen is playing with blocks. She arranges stacks of blocks so that each successive level of blocks has 1 fewer block than the level below it and the top level has 1 block. The level shown has 3 levels with 3 blocks on level 3, 2 blocks on level 2 and one block on level 1. Carmen wants to make such a stack with 12 levels. How many blocks would she use to build this stack?
Answer by Theo(13342) (Show Source):

You can put this solution on YOUR website!
if it's two dimensional, then it's a simple matter of adding additional block for each level.
1,2,3,4,5,6,7,8,9,10,11,12
add them up and you get 78 total.

this is also an arithmetic series.

An is the nth term in the series.
A1 is the first term in the series.
n is the number of terms in the series.
d is the common difference.

in your series:
A1 = 1
An = 12
n = 12
d = 1

replace the variables in the formulas with their values and you get:
12 = 1 + 11 * 1 which becomes 12 = 12 which is true.
the formula is good.

there's a sum formula as well.
that formula is Sn = n * (A1 + An) / 2

replace the variables with the values that you know and you get:
Sn = 12 * (1 + 12) / 2 which becomes Sn = 12 * 13 / 2 which becomes Sn = 6 * 13 which becomes Sn = 78
formula is good as well since it agrees with the manual calculations.