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Formula for consecutive, even, odd integers

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California4jx Really wants to Beat The GMAT! Default Avatar
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Formula for consecutive, even, odd integers Post Wed Aug 27, 2008 9:44 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Thought to put together all formulas at one place:


    Sum of all consecutive integers:

    N (N+1) / 2 ------- (I)
    where N is the number of terms.

    Example: 1+2+3+........ + 100
    N=100
    (I) => 100 (101) / 2
    => 50 (101) = 5050

    -----------------------------------------------------------------

    SUM OF EVEN NUMBERS:

    Formula: N(N+1)
    How to Find N = (First Even + Last Even)/2 - 1

    Example: 2+4+6+ ....... 100
    N = (2+100)/2 - 1 = 50

    Sum of first 50 positive even integers = (50)(51) = 2550
    ------------------------------------------------------------------

    SUM OF ODD NUMBERS:

    If N = number of odd terms then sum = (N)^2

    Thanked by: ELYAC Realty, engin09
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    rishi235 Rising GMAT Star Default Avatar
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    Post Wed Aug 27, 2008 9:53 am
    Nice work...
    Just to add to ur collection:

    Sum of squares of 1st n consecutive natural nos = n(n+1)(2n+1) / 6

    Sum of cubes of the 1st n consecutive natural nos. = [n(n+1)/2]^2

    California4jx Really wants to Beat The GMAT! Default Avatar
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    Post Wed Aug 27, 2008 1:09 pm
    Great .. !

    rixyroxy Just gettin' started! Default Avatar
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    Post Fri Aug 19, 2011 10:01 am
    Are these formulae tested on GMAT ?
    rishi235 wrote:
    Nice work...
    Just to add to ur collection:

    Sum of squares of 1st n consecutive natural nos = n(n+1)(2n+1) / 6

    Sum of cubes of the 1st n consecutive natural nos. = [n(n+1)/2]^2

    kapilhede17 Just gettin' started! Default Avatar
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    Post Fri Jul 13, 2012 9:03 pm
    I just remember the generic formula

    Sn = n/2( 2a + (n-1)d)
    a=1st term
    d= common diff

    It saves me from remembering the formula , and all the ones mentioned are like a substitution away

    Thanked by: aalexjacob
    nthiru100 Just gettin' started! Default Avatar
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    Post Mon Nov 05, 2012 8:07 am
    Thank You Guys

    Mystiqan Just gettin' started!
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    Post Sat Jun 21, 2014 9:40 am
    Or for even:[x(x+2)]/4; and odd:[x(x+2)+1]/4...x is the greatest digit of your set.ex: out of 7,5,3,1 your x would be 7. Hope this helps. I take credit for figuring these out without any help other than referencing the first equation.

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