Number of Layers

[Guest]

150 posts are placed in layers. Each layer has one less post than the layer below. Determine number of layers if top layer has 3 posts.

Unsure how to solve.

[Baltuilhe]

Good night!

It's a sum of a arithmetic sequence.
Data:
[tex]a_1=3\\
a_n=3+(n-1).1=3+n-1=2+n\\
S_n=\frac{(a_1+a_n)\cdot n}{2}\\
150=\frac{(3+2+n)\cdot n}{2}\\
300=(5+n)n\\
n^2+5n-300=0\\
n=15\\
n=-20[/tex]

So, solution is 15 layers!

Hope to Have Helped (3H)

[Guest]

Good night!

Thanks again.