SOLUTION: There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top,3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on

Algebra ->  Sequences-and-series -> SOLUTION: There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top,3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on      Log On


   

Question 898128: There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top,3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is..?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Layer Number__________Balls in Layer
1_______________________1
2_______________________3
3_______________________6
4______________________10
5______________________15__________added 5
6______________________21__________added 6
.
.
n__________________sum of 1 to n, the number of balls in a layer.

sum%28i%2C1%2Cn%29, the number of balls in the layer at index n.

The formula for this kind of summation is %28n%2F2%29%28First%2BLast%29 for the SEQUENCE on which the summation is based.

highlight%28%28n%2F2%29%281%2Bn%29=8436%29.
Solve for n, which is also the number of horizontal layers.