# Math Help - generalizing pictorial growth pattern

1. ## generalizing pictorial growth pattern

This problem is for my algebra for elementary teachers class and I am stumped!
See attachment
I am looking for an explicit formula

2. One line of triangles takes 3 toothpicks
Two lines of triangles takes 9 toothpicks
Three three lines of triangles takes 18 toothpicks

How many toothpicks does it take to make 4? Can you find a pattern?

Hint: The differences between the terms form an arithmetic series

Spoiler:

# of toothpicks = $\frac{3n(n+1)}{2}$ where n is the number of lines of triangles

3. right, I got that, but I am looking for an EXPLICIT formula for the number of line segments needed for the nth figure.

4. oh ok...nevermind. Thank you so much!