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Math Help - Finding Nth Term

  1. #1
    Junior Member
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    Post Finding Nth Term

    Dear Forum , I have to Find the nth term of the geometric sequence for the following,

    8,-4/3,2/9...

    I was curious if my following work is correct , please let me know what you think:

    8,(-4)/(3),(2)/(9)

    Remove all extra parentheses from the expression.
    8,-(4)/(3),(2)/(9)

    This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by -(1)/(6) gives the next term. In other words, an=r*an-1.
    Geometric Sequence: r=-(1)/(6)

    This is the form of a geometric sequence.
    an=a1r^(n-1)

    Substitute in the values of a1=8 and r=-(1)/(6).
    an=8*(1)/(6^(n-1))

    Multiply 8 by (1)/(6^(n-1)) to get (8)/(6^(n-1)).
    an=(8)/(6^(n-1))

    Substitute in the value of n to find the nth term.
    a2=(8)/(6^((2)-1))

    Remove the parentheses around the expression 2.
    a2=(8)/(6^(2-1))

    Subtract 1 from 2 to get 1.
    a2=(8)/(6)

    Reduce the expression (8)/(6) by removing a factor of 2 from the numerator and denominator.
    a2=(4)/(3)
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  2. #2
    MHF Contributor

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    That is the correct basic idea. But you forgot the signs.
    8\left(\frac{{\color{red}-}1}{6}\right)^{n-1}
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