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Math Help - Arithmetic Sequences

  1. #1
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    Thumbs up Arithmetic Sequences

    The sum of the first 20 terms of an arithmetic sequence is p, and the sum of the first 22 is q. Write down expressions for the common difference, and the sum of the first 18 terms.

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  2. #2
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    Re: Arithmetic Sequences

    For starters, can you set up two equations from the two first two bits of information?
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  3. #3
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    Re: Arithmetic Sequences

    S2o=p
    S22=q
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    Re: Arithmetic Sequences

    Remember nth term of an AP is given by = a + ( n-1) d where a is the first term and d the common difference.
    Thus you have
    a + 21 d = q and a + 19d = p
    I am sure now you know what to do further
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  5. #5
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    Re: Arithmetic Sequences

    I know you have to use the equation: Sn= n/2 (a+ (n-1) d)
    I'm still so confused, sorry!!
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  6. #6
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    Re: Arithmetic Sequences

    That is right, The formula for the sum of n terms of an AP is Sn= n/2 [ 2a + ( n-1) d ] Note that it should be 2a and not a.
    So there is nothing left for now you have
    10 [ 2a+19 d ] = p and 11 [ 2a + 21 d ] = q. now find a the first term and d the common difference and get the result.
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