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Math Help - Find the first 5 terms

  1. #1
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    Find the first 5 terms

    Find the first five terms of the recursively defined sequences bellow,

    a. a1 = 1, an+1=1 + 1/n

    b. a1=2, a2=3,a3= 4, an-1 + an-3

    c. a1=2, an+1=an!

    Thx in advance!
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  2. #2
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    What have you done?
    Where do you have a problem?
    There are very straight forward!
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  3. #3
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    uhm.. for a. what does it mean by 'first 5 terms?' is that n+1, n+2.. n+5?
    for b. what are the first 5 terms...? anf for c. also i dont know what the first 5 terms are
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by arturju View Post
    Find the first five terms of the recursively defined sequences bellow,

    a. a1 = 1, an+1=1 + 1/n
    Quote Originally Posted by arturju View Post
    uhm.. for a. what does it mean by 'first 5 terms?' is that n+1, n+2.. n+5?
    for b. what are the first 5 terms...? anf for c. also i dont know what the first 5 terms are
    I'll do the first one as an example and I would recommend you do the other two and post them. That way we can check your work and correct any mistakes you may have made.

    a) a_1 = 1, a_{n+1} = 1 + 1/n

    In general this series is defined as the set of numbers:
    a_1, a_2, a_3, ...

    The first 5 terms of the series would then be:
    a_1, a_2, a_3, a_4, and a_5.

    By the definition above, the first term, a_1, is given by
    a_1 = 1.

    Again, by the definition above, a_2 is given by the n = 2 term a_n = 1 + 1/n for n = 2. So:
    a_2 = 1 + 1/2 = 3/2

    Similarly
    a_3 = 1 + 1/3 = 4/3

    a_4 = 1 + 1/4 = 5/4

    a_5 = 1+ 1/5 = 6/5

    So the first five terms of the series are:
    1, 3/2, 4/3, 5/4, and 6/5.

    You should consult your textbook to make sure you understand what the different words mean (such as what a "term" of a series is) to help you out.

    -Dan
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  5. #5
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    if the first five terms for the 1st one are as you said, then for the 2nd one wouldnt i have tu find just the next one?
    Nevertheless, i worked on the problem and i got this:

    b. a1=2, a2=3,a3= 4, an-1 + an-3

    ~~~~~~~~~~~~~~~~~~~~~
    a4=a4-1+a4-3=4+2=6
    a5=a5-1+a5-3=6+3=9
    a6=a6-1+a6-3=9+4=13
    a7=a7-1+a7-3=13+6=19
    ...and so on..
    I think i did problem c. wrong but i'll post it here anyways:
    c. a1=2, an+1=an!
    ~~~~~~~~~~~~~~~~~~~~~
    a2=a1+1=a1!=2
    a3=a2+1=a2!=2
    ... and so i got 2 for all of them..
    I have another problem like this i'm having trouble with but i'd rather post it after i get this one over with. Thx in advance

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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by arturju View Post
    if the first five terms for the 1st one are as you said, then for the 2nd one wouldnt i have tu find just the next one?
    Nevertheless, i worked on the problem and i got this:

    b. a1=2, a2=3,a3= 4, an-1 + an-3

    ~~~~~~~~~~~~~~~~~~~~~
    a4=a4-1+a4-3=4+2=6
    a5=a5-1+a5-3=6+3=9
    a6=a6-1+a6-3=9+4=13
    a7=a7-1+a7-3=13+6=19
    ...and so on..
    I think i did problem c. wrong but i'll post it here anyways:
    c. a1=2, an+1=an!
    ~~~~~~~~~~~~~~~~~~~~~
    a2=a1+1=a1!=2
    a3=a2+1=a2!=2
    ... and so i got 2 for all of them..
    I have another problem like this i'm having trouble with but i'd rather post it after i get this one over with. Thx in advance

    i only examined c since you said you weren't sure about that. it's correct. you can post the next problem in a new thread
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    b looks ok too
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