Question 1195799
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Here's a similar problem.


Consider the sequence 1, 2, 4, ...


One assumption is that the next term could be 7 because:
The jump from 1 to 2 is +1
The jump from 2 to 4 is +2
If we kept this pattern going, then the next jump would be +3 and we'd get 4+3 = 7
After that, the next term is 7+4 = 11, and so on.
So we might have 1, 2, 4, 7, 11, ...


Side note: The generating polynomial for this would be y = 0.5x^2 - 0.5x + 1, if the previous paragraph's assumptions were true.


Or, the next term could be 8 since the original three terms appear to show the powers of 2
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
and so on
Put another way, the jump from term to term might be "multiply by 2".


Or maybe there's some recursive method we could use to build those first three terms.
Maybe we could say: To generate the next term, add the previous two terms, then add 1
term3 = (term1)+(term2)+1 
term3 = (1)+(2)+1 
term3 = 4
then,
term4 = (term2)+(term3)+1
term4 = (2)+(4)+1
term4 = 7
and,
term5 = (term3)+(term4)+1
term5 = (4)+(7)+1
term5 = 12
Under this process we have the sequence 1, 2, 4, 7, 12, ...
It somewhat resembles the Fibonacci sequence.


I'm sure you could get creative in a number of ways to generate the next term. 


To summarize, we could have these sequences
1, 2, 4, 7, 11, ...
1, 2, 4, 8, 16, ...
1, 2, 4, 7, 12, ...
Likely there are infinitely others. 


The punchline here is that problems asking about the next term are often too vague. 
When things are vague, multiple answers are possible. It's like saying "I'm thinking of a round thing", and another person asking "is that a rock? a ball? a marble? a wheel?". 
There's simply not enough information.


It's why the other tutors consider this problem to be "nonsense". I agree somewhat.
If there was context like "this sequence is arithmetic" or "the sequence is polynomial", then it would be much more clear and would provide one single definitive answer.


With that said, there might be the implication the sequence could be polynomial. In that it follows a fourth degree polynomial form that @greenestamps mentioned. Of course this is purely speculative based on my experience with problems of this nature. 


I would ask your teacher for further clarification.
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