Question

A clerk in the sports department of a store is stacking tennis balls in the shape of a square pyramid. The top layer has 1 ball, the second layer has 4 balls, the third layer has 9 balls, and so on, as shown below.

Which of the following represents the number of balls in the first 8 layers of the pyramid?
A. a series that is arithmetic
B. a series that is geometric
C. a series that is neither arithmetic nor geometric
D. a series cannot be used to represent this situation.

Answer 1

Letter C.
The series is neither arithmetic or geometric.
The pattern is
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
n^2 is the pattern where n is the position in the series.

Answer 2

It is a series that is neither arithmetic nor geometric

Explanation:

We are given that The top layer has 1 ball, the second layer has 4 balls, the third layer has 9 balls, and so on,

The pattern is

`1^2 = 1`

`2^2 = 4`

`3^2 = 9`

`4^2 = 16`

n^2 is the pattern where n is the position in the series.

For arithmetic series Common difference:
`d=a_2-a_1=a_3-a_2`

So,
`d=4-1\\eq 9-4`

Thus it is not an arithmetic series .

For Geometric series there must be an common ratio :
`r = (a_2)/(a_1)=(a_3)/(a_2)`

So,
`r = (4)/(1)\\eq(9)/(4)`

Thus it is not geometric series.

Thus Option C is correct.

It is a series that is neither arithmetic nor geometric