Number of balls in 1st layer = 1 Number of balls in 2nd layer =3=1+2 Number of balls in 3rd layer = 6=1+2 + 3 Number of balls in 4th layer =10=1+2+3+4 Now, the nth term =
n(n+1)
2
=
n2
2
+
n
2
Sum of n terms of series =
1
2
[Σn2+Σn] =
1
2
[
n(n+1)(2n+1)
6
+
n(n+1)
2
] =
n(n+1)(n+2)
6
Now ,
n(n+1)(n+2)
6
= 8436 or n (n + 1) (n + 2) = 50616 The above condition is satisfied only for n = 36