Answer:
1/9
Step-by-step explanation:
The given sequence is a Geometric Sequence. A geometric sequence is defined as such a sequence in which each successive term is obtained by multiplying the previous term by a fixed number known as common ratio.
How to identify a geometric sequence?
Divide any two consecutive terms of the sequence, if the ratio of terms stay the same then the sequence is a geometric sequence.
For the given sequence:
First term = 9
Second term = 3
Third term = 1
Fourth term = 1/3
Ratio of 2nd term to 1st term = 3/9 = 1/3
Ratio of 3rd term to 2nd term = 1/3
Ratio of 4th term to 3rd term = 1/3
Since the ratio is common (equal to 1/3), the given sequence is a geometric sequence. The next term(5th term) will be obtained by multiplying the previous term(4th term) with the common ratio(1/3)
So, the 5th term will be:
1/3 x 1/3 = 1/9
