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Math Help - explanation of formula for sum of sequence

  1. #1
    Junior Member
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    explanation of formula for sum of sequence

    The question ask to find a formula for the sum of the first n terms of the sequence

    9,13,17,21,....

    So the answer is Sn= n(2n + 7)

    Can someone explain why would this arithmetic sequence of sum not look like the usual formula, that is Sn= [n(a1 + an)] / 2

    I think Im missing a key point in understanding whats going on here.

    Thanks in advance
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  2. #2
    MHF Contributor
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    ukgwan,

    if you try your formula S_n = 0.5n(a_1 + a_n), you'll see that it actually works. The problem is that to do yours, you need to know the values of a_1 and a_n.


    The textbook solution S_n = n(7 + 2n) is quicker, because you just input n and get the answer directly.


    Your not missing anything conceptual here, if you work out a formula for a_n, and then subsititute it into your method, you will get the textbook answer.

    a_n = 5+4n
    S_n = 0.5n(a_1 + a_n)
    S_n = 0.5n(9 + (5+4n))
    S_n = 0.5n(14 + 4n)
    S_n = n(7 + 2n)
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  3. #3
    Junior Member
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    Smile

    That was a excellent explanation!! You would make a good professor someday.
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