I rewrote the example and made it 1,4,9,16, ...
]]>"Find the rule of 1, 2, 4, 8, 16, 32, 64"
Isn't that
, not ?]]>In order to define a sequence, you need to define all its terms. You dont just list the first few terms and ask everybody else to find the rule.
But then we may as well throw the question away (and with it most IQ tests!)
And people do get asked "find the next number in the sequence", and in that case I think the simplest rule would provide the best answer (but mention that there are others).
And when we do get visitors asking questions like that it would be nice to have a page to refer them to ... so if anyone has any neat tricks to include, let me know.
]]>In order to define a sequence, you need to define all its terms. You dont just list the first few terms and ask everybody else to find the rule.
Technically, you're right. But I think you're missing the bigger picture. In many combinatorial problems which have solutions for n=1, 2, 3..., what you typically do is list out the first few terms, find the rule, then prove that the rule applies. Being able to "see" the rule only after the first few terms is a very important skill and one that needs to be practiced. In general, many problems in pure mathematics also work like this where you can prove it for a few simpler cases and then notice recurring themes to do the entire proof in general. This is especially true with algorithms in graph theory. Not exactly the same thing, but a close parallel.
]]>If you see a sequence beginning 1, 4, 9 how on earth can you conclude that the next term must be 16? The rule might not be x[sub]n[/sub] = n[sup]2[/sup] at all. It might be x[sub]n[/sub] = (n[sup]3[/sup]+11n−6)⁄6 instead in which case the next term is not 16 but 17.
In order to define a sequence, you need to define all its terms. You dont just list the first few terms and ask everybody else to find the rule.
PS. To understand recursion, you must first understand recursion.
You always curse before you recurse.
]]>(But maybe I should mention it beforehand ... thanks mathsy!)
]]>PS. To understand recursion, you must first understand recursion.
]]>recursive definitions are also valid, right? like the fibbonacci series.
]]>Find the next number in this sequence:
1, 4, 9, 25
Did you guess 36? Because that's wrong. The right answer is 73. The rule in this sequence is:
x_n = n^2, unless n = 5 in which case x_n = 73.
]]>Sequences and Series
Sequences - Finding The Rule
How do they look? Any mistakes?
(And, yes, not much on "Series" .. I hope to do a page or two on that in the future)
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