Odd sequences

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    Hi guys,

    So I am not a mathematician but reaaally need to solve this sequence difference for my linguistics/ semantics class.
    If I have a sequence such as {21, 22, 25, 26, 29, 30, 33, 34, 37, ...} in which the difference is always 1, 3, 1, 3, ... how could I describe this? I've been reading about the nth term and quadratic nth terms but nothing seems to fit due to the odd sequence! :confused:
    I would really appreciate some help on this!

    Jess
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    (Original post by jessicalorynn)
    Hi guys,

    So I am not a mathematician but reaaally need to solve this sequence difference for my linguistics/ semantics class.
    If I have a sequence such as {21, 22, 25, 26, 29, 30, 33, 34, 37, ...} in which the difference is always 1, 3, 1, 3, ... how could I describe this? I've been reading about the nth term and quadratic nth terms but nothing seems to fit due to the odd sequence! :confused:
    I would really appreciate some help on this!

    Jess
    Simplest way to do this is to break it up into odd and even terms. Each of these is described by a simple linear equation.
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    (Original post by Gregorius)
    Simplest way to do this is to break it up into odd and even terms. Each of these is described by a simple linear equation.
    I'm sorry I don't follow. I was thinking I can say it's a positive integer ≥ 21 but after that I just get stuck! I haven't learnt any math since I was 15/16 so this is proving as a bit of a challenge to say the least haha.
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    (Original post by jessicalorynn)
    I'm sorry I don't follow. I was thinking I can say it's a positive integer ≥ 25 but after that I just get stuck! I haven't learnt any math since I was 15/16 so this is proving as a bit of a challenge to say the least haha.
    OK, let's call the nth term of the sequence a_{n}, then observe that if n is odd we can write

    \displaystyle a_{n} = 21 + \frac{n-1}{2} \times 4

    and if n is even we can write

    \displaystyle a_{n} = 22 + \frac{n-2}{2} \times 4
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    (Original post by Gregorius)
    OK, let's call the nth term of the sequence a_{n}, then observe that if n is odd we can write

    \displaystyle a_{n} = 21 + \frac{n-1}{2} \times 4

    and if n is even we can write

    \displaystyle a_{n} = 22 + \frac{n-2}{2} \times 4
    Thanks for your help! Now a stupid question but what actually is n? Or do we have to work that out..?
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    (Original post by jessicalorynn)
    Thanks for your help! Now a stupid question but what actually is n? Or do we have to work that out..?
    You use n (or rather a_{n}) to label the sequence in order. So the first value of the sequence is a_{1}, the second is a_{2}, the third a_{3} and so on. So, for example, for your sequence:

    \displaystyle a_{3} = 25 = 21 + \frac{3 - 1}{2} \times 4
 
 
 
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