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Math Help - Finding Formula for a Number Sequence

  1. #1
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    Finding Formula for a Number Sequence

    I need to find the formula for the general term in the given sequences:



    ---------And---------



    I'm not sure how to approach this, I've looked for common differences, would it work if I used this: ?

    Thank you, I appreciate your help!
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  2. #2
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    the first one follows

     \frac{n}{(n-1)^2}~,n= 3,4,5,\dots

    the second

     \frac{1}{3n}~,n= 1,2,3,\dots
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  3. #3
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    Quote Originally Posted by pickslides View Post
    the first one follows

     \frac{n}{(n-1)^2}~,n= 3,4,5,\dots

    the second

     \frac{1}{3n}~,n= 1,2,3,\dots

    Thank you for the first one!

    As for the second, the first term corresponds to n=1, the second to n=2, etc. When n=1 your formula: n/(n-1)^2 actually divides by zero, and when n=2 it gives you 1.

    So it just needed to be adjusted to (n+2)/(n+1)^2.

    Thank you so much, you got me thinking on the right track.
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  4. #4
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    Quote Originally Posted by thebristolsound View Post

    As for the second, the first term corresponds to n=1, the second to n=2, etc. When n=1 your formula: n/(n-1)^2 actually divides by zero,
    incorrect, the formula provided for the second sequence was

    \frac{1}{3n}~,n= 1,2,3,\dots

    For n=1:~ \frac{1}{3\times 1}=\frac{1}{3} as required

    Quote Originally Posted by thebristolsound View Post
    and when n=2 it gives you 1.
    Incorrect again.

    For n=2:~ \frac{1}{3\times 2}=\frac{1}{6} as required
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  5. #5
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    Quote Originally Posted by pickslides View Post
    incorrect, the formula provided for the second sequence was

    \frac{1}{3n}~,n= 1,2,3,\dots

    For n=1:~ \frac{1}{3\times 1}=\frac{1}{3} as required



    Incorrect again.

    For n=2:~ \frac{1}{3\times 2}=\frac{1}{6} as required
    My bad, I misdirected you. I meant to thank you for the formula pertaining to the second sequence: However, as for the first sequence, I had to modify to in order for it to work when n=1 and n=2. When n=1 your formula actually divides by zero, and when n=2 it produced 1.

    Sorry for the inconvenience!
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  6. #6
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    Both notations are equivalent. The only difference is that his sequence starts with n=3 while yours starts with n=1. His formula does not divide by 0 since the first element is when n=3.
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  7. #7
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    Quote Originally Posted by thebristolsound View Post
    I had to modify to in order for it to work when n=1 and n=2. When n=1 your formula actually divides by zero,
    You didn't have to modify, my sequence starts at n=3 as stated.
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