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 = A1 + (n-1) * d
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.
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