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March 27, 2017

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An arithmetic progression has 5 terms that have a sum of 200. The sum of the last three terms added to 6 times the sum of the first two terms equals zero. What is the first term?

  • algebra 2 - ,

    a1 + a2 + a3 + a4 + a5 = 200

    6 (a1 + a2) + a3 + a4 + a5 = 0

    a1 = a1
    a2 = a1 + m
    a3 = a1 + 2m
    a4 = a1 + 3m
    a5 = a1 + 4m
    so

    5 a1 + 10m = 200
    6(2 a1+ m) + 3 a1 + 9m = 0

    a1 + 2 m = 40
    15 a1 + 15 m = 0

    m = -a1

    a1 - 2a1 = 40
    a1 = -40
    m = 40

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