Question 1208497
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There are no context clues or instructions telling us what type of sequence this is (whether it pertains to the entire fractions themselves or the pieces of the fractions).


Predicting the next term of a sequence like this is not really mathematics. 
It's purely guesswork.
The other tutors have shown there are multiple possible answers. 
There are perhaps infinitely many.


I'll provide a summary of what tutors Greenestamps and Edwin have found.
Each item in <font color=red>red</font> is a <font size=4>potential</font> answer, but there's no way of truly knowing without more context. 
It might turn out that your teacher is looking for something else entirely.
1/2, 2/3, 6/5, <font color=red>30/11</font>
1/2, 2/3, 6/5, <font color=red>30/7</font>
1/2, 2/3, 6/5, <font color=red>24/7</font>
1/2, 2/3, 6/5, <font color=red>7/8</font>
1/2, 2/3, 6/5, <font color=red>21/10</font>
It would be cruel madness for a teacher to expect students to be mind readers.



See this <a href = "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1195799.html">similar question</a>
On that link I try to find the next few terms in the sequence 1,2,4,...
It turns out there are at least 3 different possible answers for that question. There may be infinitely many answers. 
This is more evidence that vague questions like this are very flawed. There needs to be more context provided. 


A good well phrased question is something like "The sequence 1,3,5,7,... is arithmetic. What is the next term?"
A very flawed question simply gives a sequence without mentioning what type of sequence it is.
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