Given the following reaction and its intermediate steps, calculate the relation between the rate of reaction of the resultant reaction and the rates of reaction of the intermediate steps.

Question

Step-1: $2\;NO \begin{array} {c} \overset{k_1}\; \\ \large \rightleftharpoons \\\overset{k_2} \;\end{array} N_2O_2$

Step-2: $N_2O_2 + O_2 \overset{k_3} \rightarrow 2NO_2$

Overall: $ 2NO + O_2 \overset{k} \rightarrow 2NO_2$

$\begin{array}{1 1} k = \large\frac{k_1 k_3}{k_2} \\ k = \large\frac{k_1 k_2}{k_3} \\ k = \large\frac{k_1}{k_2 k_3} \\ k = \large\frac{k_3}{k_1k_2}\end{array}$