Answer:
D. 9
Step-by-step explanation:
From the question, we are given the following information:
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
In other to solve for n, we would be taking some values for n
Step 1
Let's take the first layer,
n is represented by 1
n = 1
P(1) = P(1 - 1) + 1²
P(1) = 1 tennis ball.
Step 2
Let's take the second layer
n is represented by 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
Step 3
Let's take the third layer
n is represented by 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
Step 4
Let's take the fourth layer
n is represented by 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
We can continue this process, on and on
From the above solution for the number of the tennis balls in first four layers will be: 1, 5, 14, 30,
Hence, the number of tennis balls that Coach Kunal could not have is 9.
