Question

Coach Kunal stacks all of the tennis balls in a square pyramid.

The number of tennis balls, P(n), in n layers of the square pyramid is given by P(n) = P(n – 1) + n^2.

Which could not be the number of tennis balls Coach Kunal has?

A. 30
B. 9
C. 5
D. 14

Answer 1

the correct answer is b.9

Answer 2

The correct option is: B. 9

Explanation:

The number of tennis balls,
`P(n)` , in
`n` layers of the square pyramid is given by:
`P(n)=P(n-1)+n^2`

As the stack of the tennis balls is in shape of a square pyramid, that means in the top layer, there will be one ball. So,
`P(1)= 1`

Now, if
`n=2,` then
`P(2)= P(2-1)+(2)^2 = P(1)+4=1+4=5`

If
`n=3,` then
`P(3)=P(3-1)+(3)^2=P(2)+9=5+9=14`

If
`n=4,` then
`P(4)=P(4-1)+(4)^2 = P(3)+16=14+16=30`

That means, the number of tennis balls from the top layer will be: 1, 5, 14, 30, .......

So, the number of tennis balls that Coach Kunal could not have is 9.