Answer
The value of ${{a}_{n}}=-3$
Work Step by Step
The value $f\left( 3 \right)$ gives the value of the function when $x=3$.
$f\left( 3 \right)={{a}_{n}}\left( {{\left( 3 \right)}^{4}}-3\left( {{3}^{2}} \right)-4 \right)$
Now, put $-150$ for $f\left( 3 \right)$ and solve for ${{a}_{n}}$,
$\begin{align}
& -150={{a}_{n}}\left( 81-3\cdot 9-4 \right) \\
& -150={{a}_{n}}\cdot 50 \\
& {{a}_{n}}=\frac{-150}{50} \\
& {{a}_{n}}=-3
\end{align}$
Thus, the value of ${{a}_{n}}$ is $-3$.
