Strategy of drawing the points of the sequence

AI Thread Summary
The discussion focuses on strategies for finding the general term of a sequence, with an emphasis on drawing points to visualize the sequence. While some sequences, like simple counting numbers, are easy to identify, others, such as the Fibonacci sequence, require more observation and time. Participants share that while there are limited tricks, recognizing patterns like alternating signs can be helpful. One user notes they eventually found the general term through observation but seeks more efficient methods. Overall, the conversation highlights the challenge of identifying sequence patterns and the need for effective strategies.
PPonte
I started the study of sequences some days ago and I am searching for tricks, hints, that could help me find the general term of a sequence. I am following the strategy of drawing the points of the sequence and then I try to find the expression of a function that contains those points. But, unfortunately, this is not helping me with the sequence I am dealing with right now. Would you please tell me your strategies/tricks?

Thank you. :wink:
 
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Much of the time it depends on the actual sequence. For example, the sequence 1, 2, 3, 4, 5...is easy to see by observation, but the sequence 1, 1, 2, 3, 5... (Fibonnaci) isn't as easy by inspection.
 
Thank you, daveb, altough I already knew that. I ended up finding the general term of the sequence I was dealing with, precisely, by observation. But it takes time, I need tricks :).
 
The ultimate trick : http://www.research.att.com/~njas/sequences/
 
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...interesting. But during a test I cannot use this trick :) .
 
I don't think there are too many tricks, but I would try to remember that

<br /> (-1)^{n} = 1, -1, 1, -1, 1...<br />

and

<br /> (-1)^{n+1} = -1, 1, -1, 1, -1...<br />
 

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