Alecia,HowGan

Gauss method finding the sum of 4+8+12...+200?

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3 months ago 3

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  1. Puzzling

    4 + 8 + 12 + ... + 200
    = 4(1 + 2 + 3 + ... + 50)

    For the sequence 1 + 2 + 3 + ... + 48 + 49 + 50, pair up the lowest and highest terms, then the next lowest/highest, etc. Each of those pairs add up to the same value:
    (1 + 50) + (2 + 49) + (3 + 48) + ... <-- 25 pairs
    = 51 + 51 + 51 + ... <-- 25 times
    = 51 * 25

    So 4 + 8 + 12 + ... + 200
    = 4(51 * 25)
    = 4 * 25 * 51
    = 100 * 51
    = 5100

  2. Mr.Mukherjee

    there are in all 50 numbers from 4 to 50 ( since 4x 50 = 200 ) , the arithmetic average of the number series is :
    ( 4 + 200 ) / 2 = 204 / 2 = 102 .
    so the sum of all 50 numbers : 50 numbers x average value = 50 x 102 = 5100 .

  3. D.W.

    number of terms = 200/4 = 50
    ∑ = 50(a₁ + a₅₀)/2
     = 50(4 + 200)/2
     = 50(204)/2
     = 5,100

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