In a stack of bricks, layer contains one more brick than the layer above. The top layer consists of a single brickthere are 105 bricks in the stack, how many layers are there

Answer 1

Hi, Emily,

I'm sure there is a more mathematically elegant approach, but all I did was add the numbers 1,2,3,4,5, . . . . until their cumulative sum was 105. That requires a series of 14 numbers from 1 to 14, which, when summed, is equal to 105. The numbers represent the number of brinks in each row, starting from the top and increasing by one for each layer. Easy in Excel.

Bob

Answer 2

use the formula for the sum of an arithmetic sequence

S=(n/2)(2a+[n-1]d)

a=first term which is 1

n=# of terms to be determined

d=common difference which is 1

105=(n/2)(2+[n-1]*1)

105=(n/2)(2+n-1)

210=n(n+1)

n^2+n-210=0

(n+15)(n-14)=0

n-14=0

n=14 terms or 14 layers

1,2,3,4,5,6,7,8,9,10,11,12,13,14

add them together to get 105