Let $A$ be an $\mathbb{E}_\infty$-ring spectra, and let $R_1$, $R_2$ and $R_3$ be $\mathbb{E}_\infty$-$A$-algebras.
We assume there is a homotopy sequence
$$
R_1\to R_2 \to R_3
$$ 
in a stable infinity category $\text{Mod}_{A}(\text{Sp})$.
Then is there a homotopy sequence
$$
K(R_1) \to K(R_2) \to K(R_3)
$$
in $\text{Mod}_{K(A)}(\text{Sp})$?