In a process the pressure of a gas is inversely proportional to the square of the volume. If the temperature of the gas increases, then work done by the gas

$\begin{array}{l}P\alpha \frac{1}{V^2}\Rightarrow P=\frac{k}{V^2}\Rightarrow P{V}^2=const\\ PV.V=k\Rightarrow nRTV=k\Rightarrow TV=k_1\end{array}$

Since temperature increases therefore volume decreases. Hence the work done by the gas should be negative

Alternate method

work done is polytropic process is 

$$\begin{gathered} \frac{\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)\mathrm{nR}}{1-\mathrm{x}} \mathrm{if} \mathrm{the} \mathrm{the} \mathrm{relation} \mathrm{is} {\mathrm{PV}}^{\mathrm{x}}=\mathrm{constant} \\ \mathrm{here} \mathrm{x}=2 \mathrm{and} \mathrm{temperature} \mathrm{is} \mathrm{increasing} \mathrm{so} \mathrm{workdone} \mathrm{is} \mathrm{negative} \end{gathered}$$