Side length = 1, number of toothpicks a 1=3.

The second one is four triangles and nine toothpicks.

Side length =2, number of toothpicks a2=3+2*3=9.

.....

It can be found that:

The nth picture is the side length =n,

3n toothpicks are placed on the side of the (n- 1) th figure, and the side length = n- 1.

Then an=a(n- 1)+3n, where:

an-a(n- 1)=3n

a(n- 1)-a(n-2)= 3(n- 1)

.....

a3-a2=3*3

a2-a 1=3*2

All equations add up to:

an-a 1=3(2+3+..+n)

an=a 1+3(2+3+..+n)=3( 1+2+...+n)=3n(n+ 1)/2

The nth graph has 3n(n+ 1)/2 toothpicks (3n? +3n)/2 is 1.5n+ 1.5n?