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Thread: Arithmetic progression - Please help!

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    Arithmetic progression - Please help!

    In an arithmetic progression that consists of 60 limits overall
    - The sum of first 20 limits is 200
    - The sum of the last limits is 1000
    What's the sum of all the 60 limits?

    The rule you should use is
    Sn=n/2(2a1+(n-1)d)
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  2. #2
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    Re: Arithmetic progression - Please help!

    In an arithmetic progression that consists of 60 limits overall
    by "limits", do you mean the number of terms of the arithmetic series?

    - The sum of first 20 limits is 200
    - The sum of the last limits is 1000
    I understand the first statement to be $a_1 + a_2 + ... + a_{20} = 200$

    does the second statement mean $a_{21} + a_{22} + a_{23} + ... + a_{60} = 1000$ ?

    What's the sum of all the 60 limits?
    shouldn't $S_{60} = 1200$

    ... please provide a correction if there is a misunderstanding.
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    Re: Arithmetic progression - Please help!

    Quote Originally Posted by skeeter View Post
    by "limits", do you mean the number of terms of the arithmetic series?



    I understand the first statement to be $a_1 + a_2 + ... + a_{20} = 200$

    does the second statement mean $a_{21} + a_{22} + a_{23} + ... + a_{60} = 1000$ ?



    shouldn't $S_{60} = 1200$

    ... please provide a correction if there is a misunderstanding.
    You're right, sorry English isn't my first language.
    But no unfortunately the answer is 1800
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    Re: Arithmetic progression - Please help!

    $S_{20} = \dfrac{20}{2}[2a_1 + (20-1)d] = 200$

    - The sum of the last limits is 1000
    maybe the last 20 terms? ...

    $S_{60}-S_{40} = \dfrac{60}{2}[2a_1 + (60-1)d] - \dfrac{40}{2}[2a_1 + (40-1)d]= 1000$
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    Re: Arithmetic progression - Please help!

    Quote Originally Posted by skeeter View Post
    $S_{20} = \dfrac{20}{2}[2a_1 + (20-1)d] = 200$



    maybe the last 20 terms? ...

    $S_{60}-S_{40} = \dfrac{60}{2}[2a_1 + (60-1)d] - \dfrac{40}{2}[2a_1 + (40-1)d]= 1000$

    Yes the last 20 sorry i forgot to type thaaat!
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    Re: Arithmetic progression - Please help!

    Quote Originally Posted by Mustafashama View Post
    Yes the last 20 sorry i forgot to type thaaat!
    well, you have two equations with two unknowns, $a_1$ and $d$ ... solve the system.
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