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25 December, 18:21

What is the sum of the arithmetic series below?

-100 + - 95 + - 90 + - 85 + ... + - 5 + 0 + 5 + ... + 85 + 90 + 95 + 100

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  1. 25 December, 18:32
    0
    Hello:

    the common ratio is r = - 95 - (-100) = 5

    the general terme is : un = u1 + (n-1) r

    un = - 100 + (n-1) (5)

    un = - 100 + 5n-5

    un = 5n-105

    The last term is : 100

    un = 100

    5n-105 = 100

    5n = 205

    n = 41 (Number of terms)

    The last term is : u 41

    the sum is : S = (41/2) (-100+100) = 0
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