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March 29, 2017

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An arithmetic series has third term 11. The ninth term is 5 times the second term. Find the common difference.

  • math - ,

    Let the first term be called a and the common difference be called b.
    a + 2b = 11
    a + 8b = 5*(a + b) = 5a + 5b
    The last equation can be rewritten
    4a - 3b = 0
    4a + 8b = 44
    11b = 44
    b = 4
    a = 11 - 2b = 3
    The series is 3,7,11,15,19,23,27,31,35...
    Note that 35 (the ninth term) is 5 times 7

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