find the following sums a) 1+2+3+-…+200, b) 1+3+5+-…199, c)2+4+6+-+200

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find the following sums a) 1+2+3+…….+200, b) 1+3+5+…….199, c)2+4+6+….+200

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Eloise 1 month 2021-08-19T05:56:49+00:00 1 Answer 0 views 0

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    2021-08-19T05:58:15+00:00

    Step-by-step explanation:

    All of the given terms are Arithmatic progressions.

    a) 1+2+3+…+200

    The first term is 1, common difference= 2-1= 1

    using the formula= Last term= first term+ (number of terms-1)Common Difference

    200= 1+(n-1)1

    199= n-1

    n=200.

    Therefore using the formula- Sum= (n/2)(2*First term+(n-1)common difference)

    sum= 100(2+199(1))

    Sum= 100(201)

    Sum= 20100

    b)1+3+5+…+199

    First term is 1, common difference is 3-1= 2

    Using the formula stated above,

    199= 1+(n-1)2

    198= (n-1)2

    99= n-1

    Therefore n= 100

    Using the formula mentioned above,

    Sum= 100/2(2+(100-1)2)

    Sum= 50(2+198)

    Sum= 50(200)

    Sum= 10000

    c)2+4+6+…+200

    First term is 2, common difference is 4-2=2

    Using the formula stated above,

    200= 2+(n-1)2

    198= (n-1)2

    n-1= 99

    Therefore, n=100

    Using the formula mentioned above,

    Sum= 100/2(4+(100-1)2)

    Sum= 50(4+198)

    Sum= 50(202)

    Sum= 10100

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