Simple recurring sequence (1, 2, 1, 2, 1, 2, 1, 2, )

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In summary, the conversation discusses finding a symbolic representation for a sequence that alternates between 1 and 2. Several potential solutions are suggested, including using a recurrence relation and finding an expression for 0, 2, 0, 2, ... which can then be used to find an expression for 0, 1, 0, 1, 0, ... and eventually for 1, 2, 1, 2, 1, .... The solution of 1.5 + (0.5)(-1)^n is also mentioned. The conversation ends with the acknowledgement that the question may seem trivial.
  • #1
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trivial yet my mind is blank, I'm wayyy overthinking this!

Was just thinking of a simple sequence to test-drive on my calculator, and this one came up in my mind (the sequence terms, not the sequence itself...)

I've been trying for the past hour to find a simbolic representation of a sequence that will spit out: 1, 2, 1, 2, 1, 2...

The farthest I got so far is to get it to give back 0, 2, 0, 2 with this:

[itex]a_{n} = 1+(-1)^{n}[/itex]

From [tex]a_{1}[/tex] to [tex]a_{5}[/tex] it gives me: 0, 2, 0, 2, 0

I know it's probably the easiest thing in the world...
 
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  • #2
1.5+0.5=2, 1.5-0.5=1
 
  • #3
If you can find an expression for 0, 2, 0, 2, ... you should be able to find one for 0, 1, 0, 1, 0, ... If you can find one for 0, 1, 0, 1, 0, ... you should be able to find one for 1, 2, 1, 2, 1, ...

Alternately, it's a recurrence relation with a_{n+1} = 3 - a_n. You can find a second-order homogeneous recurrence relation if you prefer.
 
  • #4
so they would be saying 1.5 + (0.5)(-1)^n
 
  • #5
dacruick said:
so they would be saying 1.5 + (0.5)(-1)^n

Naturally! Thanks very much guys and sorry for the trivial question.
 

What is a simple recurring sequence?

A simple recurring sequence is a pattern of numbers that repeats itself indefinitely. In this case, the sequence is 1, 2, 1, 2, 1, 2, 1, 2, and so on.

What is the rule for the sequence?

The rule for this sequence is to alternate between 1 and 2.

How can this sequence be represented mathematically?

This sequence can be represented as a_n = 1 + (-1)^n, where n is the position of the term in the sequence.

What is the significance of simple recurring sequences in mathematics?

Simple recurring sequences are important in mathematics because they can be used to model real-world phenomena, such as the growth of populations or the oscillation of a pendulum. They also have applications in number theory and cryptography.

Is this sequence considered a "chaotic" sequence?

No, this sequence is not considered chaotic as it follows a predictable pattern and does not exhibit sensitive dependence on initial conditions, which is a key characteristic of chaotic systems.

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