10. If $\left\{a_{n}\right\}$ is an increasing sequence, and for any positive integer $n, a_{n}=n^{2}+\lambda n$ always holds, then the range of the real number $\lambda$ is $\qquad$ .
10. $(-3,+\infty)$.
$a_{n+1}-a_{n}=2 n+1+\lambda>0$, for all $n \in \mathbf{N}_{+}$ to hold, it is sufficient that $3+\lambda>0$, then $\lambda>-3$.