The next number in the pattern would be 1/4
The sequence above is a geometric sequence whose common ratio is 3.
1/324, 1/108. 1/36, 1/12, 1/4, ................
Further Explanation;
Sequence
- A sequence refers to a set of numbers, called terms, arranged in some particular order.
- There are two major types of sequences.
Arithmetic sequence
- An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference (d).
- For example;
2,4,6,8,10,12,.............. is an arithmetic sequence with a common difference of 2.
- The nth term of an arithmetic series is therefore given by;
[tex]a_{n} =a_{1} + (n-1)d[/tex]
Where [tex]a_{1}[/tex] is the first term and d is the common difference.
Geometric sequence
- A geometric sequence is a sequence with the ratio between two consecutive terms constant.
- The sequence follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
1/324, 1/108. 1/36, 1/12, 1/4, ................ is a geometric sequence in which the common ratio is 3.
The nth term of a geometric sequence is given by;
[tex]a_{n} =a_{1} r^{n-1}[/tex]
where [tex]a_{1}[/tex] is the first term and r is the common ratio
Key words: sequence, arithmetic sequence, geometric sequence, common difference, common ratio
Learn more about;
- Arithmetic sequence: https://brainly.com/question/4694425
- Geometric sequence: https://brainly.com/question/4694425
- Example of a geometric sequence: https://brainly.com/question/4694425
Level: High school
Subject: Mathematics
Topic: Sequence and series
Sub-topic: Geometric sequence
