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Help on an arithmetic progression question watch

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    The sum of the first ten terms of an AP is 95, and the sum of the first 20 terms of the same AP is 290. Calculate the first term and the common difference.

    I've done

    S_{10}=5[2a+9d]=95
    S_{20}=10[2a+19d]=290

    Thought about simultaneous equation, tried it but it didn't really come to much..
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    2a+19d=29
    2a+9d=19

    dont look the hardest simul equations to solve.
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    (Original post by mathz)
    2a+19d=29
    2a+9d=19

    dont look the hardest simul equations to solve.
    How did you get the 29 and 19?

    From what I can see you divided one by 5 and the other by 10

    :confused:
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    (Original post by Kash:))
    How did you get the 29 and 19?

    From what I can see you divided one by 5 and the other by 10

    :confused:
    That's exactly what he did.
    If:
    5(2a + 9d) = 95
    and
    10(2a + 19d) = 290

    Then:
    2a + 9d = \frac{95}{5} = 19
    {lets call this #1}
    and
    2a + 19d = \frac{290}{10} = 29
    {lets call this #2}

    Now let's take #1 from #2 and end up with:
    10d = 10

    And subsitute d into one of the equations above to find a.
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    (Original post by Wednesday Bass)
    That's exactly what he did.
    If:
    5(2a + 9d) = 95
    and
    10(2a + 19d) = 290

    Then:
    2a + 9d = \frac{95}{5} = 19
    {lets call this #1}
    and
    2a + 19d = \frac{290}{10} = 29
    {lets call this #2}

    Now let's take #1 from #2 and end up with:
    10d = 10

    And subsitute d into one of the equations above to find a.
    Thanks, just saw it :top:
 
 
 
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