Oranges are stacked as a triangularbased pyramid such that t

Oranges are stacked as a triangular-based pyramid such that there is one orange on the top, 2 more oranges on the second layer, yet 3 more oranges on the third, and so on until there are 200 pyramidal layers of oranges. If this big lot is distributed into boxes of 7 oranges each, how many oranges will remain undistributed?

Solution

first row = 1 orange

secod row = 1+2 =3 oranges

third row = 3+3=6 oranges

fourth row = 6+4 = 10 oranges

and so on

in general there will be n+n(n-1)/2 oranges in the row n

so in the 200 th row there is 200 +199X200/2 =20100 oranges

hence total number of oranges is 135300

hence when divided by 7 we get that 6 oranges are left without being distributed