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Math Help - Arithmetic Sequences

  1. #1
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    Arithmetic Sequences

    What is the sum of the first 100 terms of this sequence: 5, 11, 17, 23...?
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    Re: Arithmetic Sequences

    What is your first term? and what is your common difference?
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    Re: Arithmetic Sequences

    I know how to calculate this but according to a site, my calculations are wrong. I did 5 + 6*99 which indicates the final term. Adding the final term to the first term 599+5 and dividing that by 2, would be the average. The number of terms as stated is 100, so the answer should be 302 * 100, but according to the site, that's not the answer, so I don't know what I did wrong here.
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    Re: Arithmetic Sequences

    The sum of an arithmetic sequence is given by S_n = \dfrac{n}{2}(2a + (n-1)d) where

    • n is the number of terms
    • a = U_1 which is the first term
    • d is the common difference (between terms)


    You are told that n=100 and it's not hard to see that a=5. Now all that's left is to find the common difference and then plug into the formula at the top of this post.


    L'edit: Google Calculator gives 30,200 as a answer which is evidently the same as 302*100
    Last edited by e^(i*pi); July 2nd 2011 at 01:41 PM. Reason: see post
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  5. #5
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    Re: Arithmetic Sequences

    Quote Originally Posted by Saphira View Post
    What is the sum of the first 100 terms of this sequence: 5, 11, 17, 23...?
    5+[5+6]+[5+(2)6]+[5+(3)6]+....+[5+(99)6]

    =(100)5+6(1+2+3+....+99)

    =500+6[(50-49)+(50-48)+.....+50+....+(50+48)+(50+49)]

    =500+6(99)50

    However, you are probably expected to use the general formula for summing an arithmetic series,
    having recognised the series as "arithmetic"
    from the constant difference between terms.
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    Re: Arithmetic Sequences

    Quote Originally Posted by Saphira View Post
    I know how to calculate this but according to a site, my calculations are wrong. I did 5 + 6*99 which indicates the final term. Adding the final term to the first term 599+5 and dividing that by 2, would be the average. The number of terms as stated is 100, so the answer should be 302 * 100, but according to the site, that's not the answer, so I don't know what I did wrong here.
    6*99= 6(100- 1)= 600- 6= 594, not 599.
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  7. #7
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    Re: Arithmetic Sequences

    Quote Originally Posted by HallsofIvy View Post
    6*99= 6(100- 1)= 600- 6= 594, not 599.
    5+6*99 is the final term, which is 599.
    Then Saphira is calculating the average of all the terms
    by averaging the first and last terms, which are 5 and 599,
    as the sum may be evaluated using

    sum=(average)(number of terms).
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