The oxidation state of chromium in the final product formed in the reaction between KI and acidified $K_2Cr_2O_7$ solution is:
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In acidic solutions, $Cr_2O_7^{2-}$ (orange) is reduced to $Cr^{3+}$ (green). In basic solutions, $CrO_4^{2-}$ (yellow) is reduced to $Cr(OH)_3$ (green precipitate).
Acidified dichromate ($\text{Cr}_2\text{O}_7^{2-}$, Cr is $+6$) acts as a strong oxidizing agent.
It oxidizes $\text{I}^-$ to $I_2$, and is itself reduced.
The balanced ionic reaction in acidic medium is: $Cr_2O_7^{2-} + 6I^- + 14H^+ \to 2Cr^{3+} + 3I_2 + 7H_2O$.
The final product containing chromium is $Cr^{3+}$.
The oxidation state of chromium is $+3$.