Question

What would be the next number in the pattern? 1/324 1/108 1/86 1/12

Answer 1

1/4
Your teacher wrote it wrong. 1/86 should be 1/36. The pattern is dividing the denominator by 3.

Answer 2

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;  

$a_{n} =a_{1} + (n-1)d$

Where $a_{1}$ 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.

• For example;  in our case

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;  

$a_{n} =a_{1} r^{n-1}$

where $a_{1}$ 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: brainly.com/question/4694425
• Geometric sequence: brainly.com/question/4694425
• Example of a geometric sequence: brainly.com/question/4694425

Level: High school  

Subject: Mathematics  

Topic: Sequence and series  

Sub-topic: Geometric sequence