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Thread: Use sigma notation to represent each of the following

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    Use sigma notation to represent each of the following

    1+6+11+...+(5p-4)

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    Re: Use sigma notation to represent each of the following

    Quote Originally Posted by poppyisloveinthewind View Post
    1+6+11+...+(5p-4)


    or, if you prefer:



    or even:

    Last edited by Drongoski; 18 Jun 2017 at 9:50 AM.
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    Re: Use sigma notation to represent each of the following

    Quote Originally Posted by Drongoski View Post


    or, if you prefer:



    or even:

    was this done through trial and error

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    Re: Use sigma notation to represent each of the following

    Quote Originally Posted by poppyisloveinthewind View Post
    was this done through trial and error
    No no - not by trial-&-error. As I am very well-versed with the use of the sigma notation, this is nothing to me. It may take you a while to get used to it. Don't be discouraged.
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    Re: Use sigma notation to represent each of the following

    Quote Originally Posted by Drongoski View Post
    No no - not by trial-&-error. As I am very well-versed with the use of the sigma notation, this is nothing to me. It may take you a while to get used to it. Don't be discouraged.
    I thought it was +5 for some reason and hence couldnt solve it

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    Re: Use sigma notation to represent each of the following

    right i think i get it now, the answer is in the question and by using the last value you have to do trial and error, am i right?

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    Re: Use sigma notation to represent each of the following

    What trial & error?

    My 1st and 2nd versions are simply a shorthand for:

    (5x1 - 4) + (5x2 - 4) + (5x3 - 4) + . . . + (5xp - 4)


    In this case we can express any term of the sum by a formula based on the term number. For this question, the general term is 5n-4 for the nth term. On the other hand, if you want to express 1 + 67 -5 + 1 + 87 +9 - 92 + 109 -55 -13 + 27 + 16 you won't be able to write this down in a sigma notation.
    Last edited by Drongoski; 18 Jun 2017 at 1:52 PM.
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    Re: Use sigma notation to represent each of the following

    Quote Originally Posted by poppyisloveinthewind View Post
    was this done through trial and error
    Last edited by InteGrand; 18 Jun 2017 at 1:08 PM.
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    Re: Use sigma notation to represent each of the following

    Quote Originally Posted by poppyisloveinthewind View Post
    right i think i get it now, the answer is in the question and by using the last value you have to do trial and error, am i right?
    In simple terms, you need to recognise that the sequence is arithmetic, which can be proven by checking that T2 - T1 = T3 - T2.
    Ok, now that is done, we need to find Tn. Using the formula for an arithmetic sequence, Tn = a + d(n - 1), we get Tn = 1 + 5(n - 1) = 5n - 4.

    Now, we just need to fill in the sigma part! So, on the bottom, we get n = 1, because 1 is the first term (sub n = 1 into Tn to see why). On the top, since it is clear that the last term of the sequence that's being added is the pth term, p is placed on the top of the sigma. Finally, we just put 5n - 4 right next to the sigma (you can put brackets around 5n - 4 if you want to make it unambiguous).
    See below for the answer.

    Sigma Question.gif

    Hence, no trial and error is needed AT ALL.
    Last edited by bujolover; 18 Jun 2017 at 1:07 PM.
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