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An arithmetic sequence has a first term of 0 and a 10th term of 15. If 10 is an output of the sequence, which term number is it? Show and explain how you know you have the correct answer.

  • Math -

    the general term of an AS is
    a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms

    so :
    a = 0
    a+9d = 15
    0+9d = 15
    d = 15/9 = 5/3

    For 10 to be one of the terms
    a + (n-1)d = 10
    0 + (n-1)(5/3) = 10
    times 3:
    5(n-1) = 30
    5n-5 = 30
    5n = 35
    n = 7

    check:
    term(7) = a+6d
    = 0 + 6(5/3) = 10
    All is good!

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