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. 5 C. 14 D. 9

Answer 1

D. 9

Explanation:

We are told in the question that: The number of tennis balls represented by P(n), in n layers of the square pyramid is given as

P(n) = P(n - 1) + n²

Let's take the first layer

n = 1

P(1) = P(1 - 1) + 1²

P(1) = 1 tennis ball.

It is important to note that the first layers we have one tennis ball.

Let's take the second layer

n = 2

P(2) = P(2 - 1) + 2²

P(2) = P(1) + 2²

Note that: P(1) above = 1

P(2) = 1 + 2²

P(2) = 5 tennis balls

It is important to note that the second layer we have five tennis balls

Let's take the third layer

n = 3

P(3) = P(3 - 1) + 3²

P(3) = P(3 - 1) + 3²

P(3) = P(2) + 3²

Note that: P(2) above = 5

P(3) = 5 + 3²

P(3) = 14 tennis balls

It is important to note that the second layer we have fourteen tennis balls

Let's take the fourth layer

n = 4

P(4) = P(4 - 1) + 4²

P(3) = P(4 - 1) + 4²

P(3) = P(3) + 4²

Note that: P(3) above = 14

P(3) = 14 + 4²

P(3) = 30 tennis balls

It is important to note that the fourth layer we have thirty tennis balls

Hence, the number of tennis balls from the first four layers will be: 1, 5, 14, 30,

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