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.

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.

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wifilethbridge wifilethbridge · Answer 2 · 2019-04-16T09:25:53+02:00

Answer:

It is a series that is neither arithmetic nor geometric

Step-by-step 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

[tex]1^2 = 1[/tex]

[tex]2^2 = 4[/tex]

[tex]3^2 = 9[/tex]

[tex]4^2 = 16[/tex]

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

For arithmetic series Common difference: [tex]d=a_2-a_1=a_3-a_2[/tex]

So, [tex]d=4-1\neq 9-4[/tex]

Thus it is not an arithmetic series .

For Geometric series there must be an common ratio : [tex]r = \frac{a_2}{a_1}=\frac{a_3}{a_2}[/tex]

So, [tex]r = \frac{4}{1}\neq\frac{9}{4}[/tex]

Thus it is not geometric series.

Thus Option C is correct.

It is a series that is neither arithmetic nor geometric