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Thread: arithmetic sequence, determine sum

  1. #1
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    arithmetic sequence, determine sum

    In an arithmetic sequence, the fifth is 21 and the eighth is 3.
    Determine

    a) the first number of the sequence
    b) the sum of the sixteen first numbers.


    a) I got the answer to 45. So a1=45

    But I can't solve b, because I get a completely different answer than what I should get. (the answer should be 0)

    I thought:

    n=16
    a1=45
    d=-6

    an=a1+(n-1)*d

    an=45+(16-1)*(-6)

    an=45-90

    an=-45

    sum=(n/2)*(a1+an)

    sum=(16/2)*(16+(-45))

    sum=8*(-29)= -232

    so I got the sum to -232, but it should be 0. How did I think wrong?
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  2. #2
    Member Cervesa's Avatar
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    Re: arithmetic sequence, determine sum

    Quote Originally Posted by selin View Post
    In an arithmetic sequence, the fifth is 21 and the eighth is 3.
    Determine

    a) the first number of the sequence
    b) the sum of the sixteen first numbers.


    a) I got the answer to 45. So a1=45

    But I can't solve b, because I get a completely different answer than what I should get. (the answer should be 0)

    I thought:

    n=16
    a1=45
    d=-6

    an=a1+(n-1)*d

    an=45+(16-1)*(-6)

    an=45-90

    an=-45

    sum=(n/2)*(a1+an)

    sum=(16/2)*(16+(-45))

    a1 is not 16, should be (16/2)*[45 + (-45)]

    sum=8*(-29)= -232

    so I got the sum to -232, but it should be 0. How did I think wrong?
    see correction above
    Thanks from topsquark
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  3. #3
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    Re: arithmetic sequence, determine sum

    Quote Originally Posted by Cervesa View Post
    see correction above
    Thank you.
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