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arithmetic

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find the common difference of A.P whose first term is 5 and the sum of its first 4 terms is half the sum of next 4 terms

  • arithmetic - ,

    Let the common difference be d.
    The sum of the first four terms is
    5 + (5+d) + (5+d+d) + (5+d+d+d)
    = 20 + 6d
    The sum of the next 4 terms is
    5+4d + 5+5d + 5+6d + 5+7d = 20 + 22d

    You have been told that
    20 +6d = (1/2)(20 + 22d)= 10 + 11d
    Therefore
    5d = 10
    d = 2

    Check: does
    5+7+9+11 = (1/2)(13+15+17+19) ?
    32 = (1/2)(64)

  • arithmetic - ,

    ask your teacher

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