If the figure in the left is figure 1, the one in the middle is figure 2 and the one in the right is figure 3, find the total number of triangles in the figure that follows this pattern.
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In figure 1, there is 1 triangle.
In figure 2, there are 4 triangles.
In figure 3, there are 9 triangles.
(For clarification):-
In figure 4, there are 1 6 triangles.
In figure 5, there are 2 5 triangles.
So, we see that in the n th figure, the total number of triangle is given by the formula n 2
So, in the 2 0 1 6 th figure, there would be 2 0 1 6 2 triangles.
= 4064256 triangles. □