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, ................
<h2>Further Explanation;
</h2><h3>Sequence
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- A sequence refers to a set of numbers, called terms, arranged in some particular order.
- There are two major types of sequences.
<h3>Arithmetic sequence
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- 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;
Where is the first term and d is the common difference.
<h3>Geometric sequence
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- 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;
where is the first term and r is the common ratio
Key words: sequence, arithmetic sequence, geometric sequence, common difference, common ratio
<h3>Learn more about;
</h3>
Level: High school
Subject: Mathematics
Topic: Sequence and series
Sub-topic: Geometric sequence