Is the following an arithmetic sequence, geometric sequence or neither: 324, 108, 36, 12, 4, ...

It follows a geometric sequence

Step-by-step explanation:

Given

Progression: 324, 108, 36, 12, 4, ...

Required:

State the type of sequence it obeys

First, we need to understand how arithmetic sequence and geometric sequence work.

A sequence is said to be arithmetic sequence if successive terms are bounded by a common difference.

The common difference is gotten by subtracting from each term, the previous term.

In other words

Common difference = 2nd term - 1st term

Common difference = 3rd term - 2nd term

Common difference = 4th term - 3rd term ... And so on

To check if the above sequence follows an arithmetic sequence, the common difference need to be calculated.

Given that

First term = 324

Second term = 108

Third term = 36

Fourth term = 12

Fifth term = 4

Using the formula of common difference stated above;

So,

Common difference = 108 - 324 = - 216

Common difference = 36 - 108 = - 72

These two values are not the same;

Hence, it doesn't follow an arithmetic sequence.

We then check if it follows a geometric sequence

A series is said to be geometric sequence if successive terms are bounded by a common ratio.

The common ratio is gotten by dividing from each term, the previous term.

In other words

Common ratio = 2nd term / 1st term

Common ratio = 3rd term / 2nd term

Common ratio = 4th term / 3rd term ... And so on

Given that

First term = 324

Second term = 108

Third term = 36

Fourth term = 12

Fifth term = 4

Using the above formula

Common ratio = 324/108 = 3

Common ratio = 108/36 = 3

Common ratio = 36/12 = 3

Common ratio = 12/4 = 3

Since, the Common ratio remains the same for each successive terms, then we'll conclude that the sequence is a geometric sequence.