Look at the number of matches first:

The first triangle used 3 pieces.

The second triangle used 9 pieces.

The third triangle is 18.

Then you can sum up:

First = zeroth +3=0+3=3.

Second time = first time +6=3+6=9

Third time = second time +9=9+9= 18

Then you can get:

The fourth = the third+12 =18+12 = 30.

Fifth = fourth+15=30+ 15=45.

Sixth = fifth+18=45+ 18=63.

Seventh time = sixth time +2 1=63+2 1=84.

According to the law obtained above, we can sum up the following formula:

N =3N(N+ 1)/2

Then the third is equal to

3*3*(3+ 1)/2=9*2= 18

Then the fifth is equal to

3*5*(5+ 1)/2= 15*3=45

Then the sixth is equal to

3*6*(6+ 1)/2= 18*3.5=63

Then one tenth is equal to

3* 10*( 10+ 1)/2=30+5.5= 165

Look at the number of triangles:

The first one consists of 1 triangles.

The second one forms three triangles.

The third one forms six triangles.

So:

The fourth composition 10 triangles.

The fifth component 15 triangles.

The nth one constitutes N(N+ 1)/2 triangles.

The tenth one consists of10 * (10+1)/2 = 55 triangles.