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

Answer is D.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

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

14If n = 4 then P(4)=P(4 - 1)+ (4) ^ 2 = P(3) + 16 = 14 + 16 = 30That means, the number of tennis balls from the top layer will be: 1, 5, 14, 30,

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