Reverse Fast forward

Probability Level 3

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


The answer is 4070307.

Ashish Menon by Ashish Menon , 20, India

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 20, 2016

The number of triangles in n th {n}^{\text{th}} case is given by the formula:-
( 2 × ∑ i = 0 n + 1 i ) + 1 (2× \displaystyle \sum_{i=0}^{n + 1} i) + 1

So, in the 2016 th {2016}^{\text{th}} figure there would be ( 2 × ∑ i = 0 2017 i ) + 1 (2× \displaystyle \sum_{i=0}^{2017} i) + 1 triangles.
=4070307 triangles. □ _\square

1 Helpful 0 Interesting 0 Brilliant 0 Confused

7 + n 2 ( 6 + ( n − 1 ) 2 ) 7 + \frac{n}{2}(6 + (n-1) 2)

This will also get the answer, here n = 2015 n=2015 .

Abhay Tiwari - 5 years, 1 month ago

Ashish, Click HERE

Abhay Tiwari - 5 years, 1 month ago

Log in to reply

Hi, I am just back, nice question, I see that you started using GeoGebra ;)

Ashish Menon - 5 years, 1 month ago

Log in to reply

Ha ha, all credit goes to you :)

Abhay Tiwari - 5 years, 1 month ago

Log in to reply

@Abhay Tiwari – Thanks! ;) Your problem was fun solving

Ashish Menon - 5 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...