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

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.

RELATED QUESTIONS
Carmen is playing with blocks. She arranges stacks of blocks so that each successive... (answered by Fombitz)

A pyramid of blocks has 26 blocks at the bottom row and 2 fewer blocks each successive... (answered by Boreal)

Rob is playing with building blocks. The top row has one block, the second row has three... (answered by psbhowmick)

The top level of a pyramid has 1 block Then next level has 3 blocks and the next level... (answered by Alan3354)

The top level of a pyramid has 1 block. The next level has 3 blocks and the next level... (answered by solver91311)

Greg has 55 blocks. He stacks up all the blocks so that each row has one less block than... (answered by fractalier)

Sam has a bucket of blocks. He has 3 yellow blocks, 10 blue blocks, 6 green blocks, 8 red (answered by stanbon,ewatrrr,bucky)

A display of blocks is arranged in a pyramid with five layers. The bottom layer has 36... (answered by jim_thompson5910)

Read the problem in the box below. See if you can figure out the most logical answer.... (answered by jim_thompson5910)