Question

please solve this question with explanation

Answer 1

Given :  In pattern 1 , there are 4 smaller triangles are shaded , In given diagram we can count four triangle in pattern 1 ( In white color )

So, Number of smaller triangle ( In white color ) in pattern 2 = 10 

And
Number of smaller triangle ( In white color ) in pattern 3 = 16

So we get series of number of  smaller triangle ( In white color ) :

4 , 10 , 16 , . . .

Here we can see that :  10 - 4 = 16 -10 = 6  , Common difference ( d  )

And first term = a = 4

That is an A.P. and we know nth term in A.P. :

Tn = a+ ( n - 1 ) d , So

T73 = 4 + ( 73 - 1 ) 6 =  4 +  72   6 = 4 + 432 =  436

Thus ,
Number of smaller triangle ( In white color ) in pattern 73 = 436 

And we count total number of smaller triangles in pattern 1 = 10

So,

Total number of smaller triangles in pattern 73 = 10 * 73 = 730

Therefore,

Total number of shaded smaller triangles in pattern 73 = 730 - 436 = 294

So,

Option ( B )                                                             ( Ans )
hope it helps... :)