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14 April, 09:29

The sum of the first five terms of an arithmetic sequence is 90 less than the sum of the next five terms. What is the absolute difference between two consecutive terms of this sequence? Express your answer as a common fraction.

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  1. 14 April, 11:06
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    18/5

    Step-by-step explanation:

    let the first term of arithmetic sequence = a and the common difference = d

    The first term = a

    second term = a + d

    third term = a + 2d

    fourth term = a + 3d

    fifth term = a + 4d

    Therefore, the sum of the first five terms = a + (a+d) + (a+2d) + (a+3d) + (a+4d) = 5a + 10d

    The next five terms are

    sixth term=a+5d

    seventh term=a+6d

    eight term=a+7d

    ninth term=a+8d

    tenth term=a+9d

    The sum of the next five terms above = (a+5d) + (a+6d) + (a+7d) + (a+8d) + (a+9d) = 5a+35d

    The sum of the first five terms is 90 less than the sum of the next five terms

    Therefore, 5a+9d+90=5a+35d

    90=35d-10d=25d

    d=90/25=18/5

    Therefore the absolute difference between consecutive terms = 18/5
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