Question

question 3 of 10
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 ( p(n) = p(n - 1) + n^2 ).
which could not be the number of tennis balls coach kunal has?
a. 14
b. 5
c. 30
d. 9

Explanation:

Step1: Define base case (n=1)

For 1 layer, $P(1)=1^2=1$

Step2: Calculate P(2) using recurrence

$P(2)=P(1)+2^2=1+4=5$

Step3: Calculate P(3) using recurrence

$P(3)=P(2)+3^2=5+9=14$

Step4: Calculate P(4) using recurrence

$P(4)=P(3)+4^2=14+16=30$

Step5: Check non-matching value

Compare options to computed $P(n)$ values: 1, 5, 14, 30. 9 is not in this set.

Answer:

D. 9