= Solution
Let $J$ label the lower rotational state and write the elementary band model as
$$
\widetilde\nu=\widetilde\nu_*+B'J'(J'+1)-B''J(J+1).
$$
Here $B'',B'$ are lower and upper <rotational constants>, in inverse centimetres; a constant term associated with upper-state <vibrational angular momentum> can be included in $\widetilde\nu_*$. The <P branch> has $J'=J-1$, and the <R branch> has $J'=J+1$.
In this model the six printed labels are assigned as
$$
\boxed{\begin{array}{c|c}
\widetilde\nu/\mathrm{cm}^{-1}&\text{branch label}\\\hline
709.04&P(1)\\
706.09&P(2)\\
703.15&P(3)\\
700.22&P(4)\\
720.91&R(2)\\
723.90&R(3)
\end{array}}
$$
The low-frequency series steps away from the central origin towards increasing lower $J$. The first two high-frequency R positions are approximately $714.96$ and $717.93\ \mathrm{cm}^{-1}$, so the labels at $720.91$ and $723.90$ correspond to $R(2)$ and $R(3)$; they are not the first two rotational transitions.
There is a physical limitation to taking this schematic model literally. A strict $l=0\to|l|=1$ bending band has $J'\geq1$, so a genuine $P(1)$ transition to $J'=0$ is forbidden. The printed $709.04$ feature has the formal $P(1)$ position of the elementary model. The numerical analysis below follows the printed line sequence; it does not infer a physically allowed $J'=0$ bending level from that feature.
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