Unreachability of Inductive-Like Pointclasses in $L(\mathbb{R})$

Hjorth proved from $ZF+AD+DC$ that there is no sequence of distinct ${\mathrm{\Sigma }}_2^1$ sets of length ${\delta }_2^1$. Sargsyan extended Hjorth’s technique to show there is no sequence of distinct ${\mathrm{\Sigma }}_{2n}^1$ sets of length ${\delta }_{2n}^1$. Sargsyan conjectured an analogous property is true for any regular Suslin pointclass in $L(R)$ – i.e. if $\kappa$ is a regular Suslin cardinal in $L(R)$, then there is no sequence of distinct $\kappa$-Suslin sets of length ${\kappa }^{+}$ in $L(R)$. We prove this in the case that the pointclass $S(\kappa )$ is inductive-like.