Answer
$a_1=-\dfrac{1}{3}$
Work Step by Step
To find the first term of the give sequence. substitute $1$ to $n$ to obtain:
$a_{1} = 5(1)-6
\\a_1=\dfrac{(-1)^1}{4^1-1}
\\a_1 =\dfrac{-1}{4-1}
\\a_1=\dfrac{-1}{3}
\\a_1=-\dfrac{1}{3}$
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