Is this a suitable title?

If the figure on the left is figure 1, the one in the middle is figure 2 and the one in the right is figure 3, find the number of triangles in the 201 6 th 2016^{\text{th}} figure that follows this pattern.


The answer is 12196800.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Ashish Menon
Apr 18, 2016

In figure 1, there are 5 5 triangles.
In figure 2, there are 16 16 triangles.
In figure 3, there are 33 33 triangles.
(For clarification):-
In figure 4, there are 56 56 triangles.
In figure 5, there are 85 85 triangles.


We see that in n th n^{\text{th}} figure, there are ( 4 × i = 1 n i ) + n 2 (4 × \displaystyle \sum_{i=1}^n i) + n^2 triangles.

So, in 2016 th {2016}^{\text{th}} figure, there would be ( 4 × i = 1 2016 n ) + 2016 2 (4 × \displaystyle \sum_{i=1}^{2016} n) + {2016}^2 triangles.
= 2016 × 6050 2016 × 6050 triangles.
= 12196800 triangles. _\square

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...