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4 February, 15:34

Let x+3, 2x+1, and 5x+2 be consecutive terms of an arithmetic sequence. find the absolute value of the common difference of the terms.

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  1. 4 February, 16:34
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    If the numbers are in arithmetic sequence, this means that the difference between the consecutive terms is equal.

    Difference between first and second terms,

    D1 = (2x + 1) - (x + 3)

    D1 = x - 2

    Difference between second and third terms,

    D2 = (5x + 2) - (2x + 1)

    D2 = 3x + 1

    Equating the differences,

    D1 = D2

    x - 2 = 3x + 1

    Transposing the variables and constants to each of the sides of the equation,

    x - 3x = 1 + 2

    -2x = 3

    Dividing the equation by - 2,

    x = - 3/2

    Substituting this value to either of the difference,

    D1 = x - 2 = (-3/2) - 2 = - 7/2

    The absolute value of the difference is 7/2. Thus, the answer is 7/2.
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