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    A) the sum of the first ten terms of an AP series is 115. the sum of the next four terms of this series is 130. find the first term and the common difference of the AP.


    from this i got S10 = 115 so

    S10 = 10/2 (2a + 9d)
    S10 = 10a + 45d

    and then the next four terms, i dont even know how to begin.
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    (Original post by ihatePE)
    A) the sum of the first ten terms of an AP series is 115. the sum of the next four terms of this series is 130. find the first term and the common difference of the AP.


    from this i got S10 = 115 so

    S10 = 10/2 (2a + 9d)
    S10 = 10a + 45d

    and then the next four terms, i dont even know how to begin.
    \displaystyle \sum_{r=11}^{14} u_r= \sum_{r=1}^{14} u_r - \sum_{r=1}^{10} u_r
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    (Original post by RDKGames)
    \displaystyle \sum_{r=11}^{14} u_r= \sum_{r=1}^{14} u_r - \sum_{r=1}^{10} u_r
    i havent gone to learn the summits yet, so that looks new for me. is there like a different way using just sums of n, simultaneous equations, nth term and whatnot?

    i dont mind if its longer.
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    (Original post by ihatePE)
    i havent gone to learn the summits yet, so that looks new for me. is there like a different way using just sums of n, simultaneous equations, nth term and whatnot?

    i dont mind if its longer.
    Your sequence isn't defined so you'd have to split the summation into 2 parts as I have shown above.

    All it says is that the summation of "the next 4 terms" is equal to the summation from the first to the 14th term, then take away the summation of the first 10 terms which you already found.
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    (Original post by RDKGames)
    Your sequence isn't defined so you'd have to split the summation into 2 parts as I have shown above.

    All it says is that the summation of "the next 4 terms" is equal to the summation from the first to the 14th term, then take away the summation of the first 10 terms which you already found.
    ah okie thanks
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    (Original post by ihatePE)
    A) the sum of the first ten terms of an AP series is 115. the sum of the next four terms of this series is 130. find the first term and the common difference of the AP.


    from this i got S10 = 115 so

    S10 = 10/2 (2a + 9d)
    S10 = 10a + 45d

    and then the next four terms, i dont even know how to begin.
    That looks good, now if the next four terms add to 130 what do the first 14 terms add to? Then repeat what you did for the first 10 and yo should have 2 simultaneous equations to solve.
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    (Original post by ihatePE)
    ah okie thanks
    Just realised you can also say S_{14}=115+130 as well and get simultaneous equations that way

    My brain doesn't work well today
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    (Original post by RDKGames)
    Just realised you can also say S_{14}=115+130 as well and get simultaneous equations that way

    My brain doesn't work well today
    but i can also work it out the way u initially did it right?


    (Original post by an_atheist)
    That looks good, now if the next four terms add to 130 what do the first 14 terms add to? Then repeat what you did for the first 10 and yo should have 2 simultaneous equations to solve.
    oh yeah, i didnt think of that
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    (Original post by ihatePE)
    but i can also work it out the way u initially did it right?




    oh yeah, i didnt think of that
    Yes my original way also works.
 
 
 
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