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?