$$\begin{aligned} &\begin{aligned} & \mathrm{S}_3=3 \mathrm{a}+3 \mathrm{~d}=54 \\ & \Rightarrow \mathrm{a}+\mathrm{d}=18 \\ & \mathrm{~S}_{20}=10(2 \mathrm{a}+19 \mathrm{~d}) \\ & \Rightarrow 10(36+17 \mathrm{~d}) \\ & \Rightarrow 1600<10(36+17 \mathrm{~d})<1800 \\ & \Rightarrow 160<36+17 \mathrm{~d}<180 \\ & \Rightarrow 124<17 \mathrm{~d}<144 \\ & \Rightarrow 7 \frac{5}{17}<\mathrm{d}<8 \frac{8}{17} \end{aligned}\\ &\text { Common difference will be natural number }\\ &\begin{aligned} & \Rightarrow d=8 \Rightarrow a=10 \\ & \Rightarrow a_{11}=10+10 \times 8=90 \end{aligned} \end{aligned}$$