Answer:
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.
