Consider the following equations:

\begin{align} \tag{1} \ce{CO2 (g) + H2O (l) &<=> H2CO3 (aq)} & K_\ce{CO2} &= 10^{-1.47}\\ \tag{2} \ce{H2CO3 (aq) &<=> H+ (aq) + HCO^-_3 (aq)} & K_1 &= 10^{-6.35}\\ \tag{3} \ce{HCO^-_3 (aq) &<=> H+ (aq) + CO^-_3 (aq)} & K_2 &= 10^{-10.33} \end{align}

I am also told atmospheric $\ce{CO2}$ is at $\pu{10^{-3.5} atm}$ and the solution is pure water.

So far I have been able to find the equilibrium equations and have got the concentration of $\ce{H2CO3}$ to be $\pu{10^{-4.97}}$. However, from this I do not know where to go in order to find the concentration of bicarbonate.