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Math Help - sum of integers

  1. #1
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    sum of integers

    Find the sum of the first 100 positive even integers. Explain how this sum can be found quickly.
    Sn = (n/2)(a1 + an)
    is that the correct formula?
    could someone please help me?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by aikenfan View Post
    Find the sum of the first 100 positive even integers. Explain how this sum can be found quickly.
    Sn = (n/2)(a1 + an)
    is that the correct formula?
    could someone please help me?
    that is the correct formula. note that we can consider an ordered list of even integers as an arithmetic sequence. we use that formula to find the sum of the terms of an arithmetic sequence. you know that a_1 = 2, and we want n = 100, so now the only thing left for you to find is a_100
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    Hello, aikenfan!

    Find the sum of the first 100 positive even integers.
    Explain how this sum can be found quickly.

    Sn = (n/2)(a1 + an)
    is that the correct formula?
    That formula will work, but I prefer the general Sum Formula:

    . . S_n \;=\;\frac{n}{2}\left[2a_1 + (n-1)d\right]

    It is more complicated, but we don't need to calculate the 100th term.


    We have: . a_1 = 2,\;d = 2,\;n = 100

    Therefore: . S_{100} \;=\;\frac{100}{2}\left[2\!\cdot\!2 + (100-1)2\right] \;=\; 10,100

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  4. #4
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    I am not sure how to calculate the 100th term?
    an = dn + c?
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    Quote Originally Posted by aikenfan View Post
    I am not sure how to calculate the 100th term?
    an = dn + c?
    you would use the formula a_n = a_1 + (n - 1)d (which is the general formula for the nth term of an arithmetic sequence) where a_n is the nth term, a_1 is the first term, n is the current number of the term, and d is the common difference. you would use the values Soroban gave

    thus to find a_{100} you would compute a_{100} = 2 + (100 - 1)(2)
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    an = dn + c

    Isn't this the same thing? I get 200 either way...
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    Quote Originally Posted by aikenfan View Post
    an = dn + c

    Isn't this the same thing? I get 200 either way...
    well, if you define c as a_1 - d, then yes. but i've never seen anyone use "c" in these formulas
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  8. #8
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    Sn = (100/2)(2+200) = 10100
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