3. Let the function $f(x)=a x^{2}+x$, it is known that
$$
f(3)<f(4) \text {, }
$$
then the range of the real number $a$ is $\qquad$ .
3. $\left(-\frac{1}{7},-\frac{1}{17}\right)$.

Since when $n \geqslant 8$, $f(n)>f(n+1)$ always holds, thus, $a\frac{7}{2}$.
Solving, we get $a>-\frac{1}{7}$.
Therefore, $a \in\left(-\frac{1}{7},-\frac{1}{17}\right)$.