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Math Help - Coursework Help Nth Term!!!

  1. #1
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    Exclamation Coursework Help Nth Term!!!

    I am confused

    I am trying to find a formula to link these numbers for a part of my GCSE coursework (i.e nth term) could someone please show me how i can do this??

    1 2 3 4 5
    3 6 10 15 21....

    I know that the numbers underneath are triangle numbers, but i am confused about nth term, and dont know how to work this out.

    so far i have done this:

    1 2 3 4 5
    3 6 10 15 21
    3 4 5 6 - Difference
    1 1 1 - Difference

    But i do not know what these numbers mean? and how you can work out the nth term from it? (does the difference being incosistant then consistant show something? like n+1 or 1n or something? PLEASE HELP!!!)i want to know how i can get the answer! so please show me HOW you can find it!

    HELP WOULD BE MUCH APPRECIATED!!!
    Thanks
    lilblob
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  2. #2
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    Captian Black can u help?

    Ahhhh...someone please help URGENTLY! captain black???? or someone??? PLEASE! im soooo confused?!?!?!?!?!?!?!
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  3. #3
    Grand Panjandrum
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    There are a number of ways of doing this, which is best depends
    upon what you are expected to do/allowed to assume.

    Quote Originally Posted by lilblob
    I am confused

    I am trying to find a formula to link these numbers for a part of my GCSE coursework (i.e nth term) could someone please show me how i can do this??

    1 2 3 4 5
    3 6 10 15 21....

    I know that the numbers underneath are triangle numbers, but i am confused about nth term, and dont know how to work this out.


    You correctly observe that the sequence you are asked to find
    the n-th term for is the sequence of triangular numbers, except
    it starts from 3 rather than 1.

    Presumably you know the formula for the n-th triangular
    number:

    T(n)\ =\ n\cdot(n+1)/2.

    Now to get this to start from 3 rather than 1, just replace
    n by (n+1) in the formula to give the n-th term of your
    sequence:

    S(n)\ =\ (n+1)\cdot(n+2)/2.


    so far i have done this:

    1 2 3 4 5
    3 6 10 15 21
    3 4 5 6 - Difference
    1 1 1 - Difference

    But i do not know what these numbers mean? and how you can work out the nth term from it? (does the difference being incosistant then consistant show something? like n+1 or 1n or something? PLEASE HELP!!!)i want to know how i can get the answer! so please show me HOW you can find it!

    HELP WOULD BE MUCH APPRECIATED!!!
    Thanks
    lilblob
    Another method: The second differences of your sequence
    are constant. This should tell you that the sequence is a
    quadratic in n. So suppose:

    S(n)\ =\ An^2+Bn+C

    Now we know that S(1) = 3, S(2) = 6, and S(3)=10. So
    we have the three simultaneous linear equations for A, B and
    C:

     A\ \ \ +\ \ B\ +\ C\ =\ 3
     4A\ +\ 2B\ +\ C\ =\ 6
     9A\ +\ 3B\ +\ C\ =\ 10

    Solving these for A, B and C will also give you the formula
    for the n-th term of your sequence.

    RonL
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  4. #4
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    Thanks! That helps a lot! You are a genius!

    lilblob
    Last edited by lilblob; November 13th 2005 at 10:27 AM.
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