= Solution
For actual complete bounce distances $D_1=4\,\mathrm m$ and $D_{n+1}=rD_n$, the <geometric series> gives
$$
\boxed{D_{\rm total}=\frac{4}{1-r}\,\mathrm m,\qquad0\leq r<1.}
$$
A natural intended estimate compares the observed first round trip with the loss-free round trip from the initially compressed position,
$$
D_{\rm ideal}=2(H_s+x)=5.13764\,\mathrm m.
$$
If the reduction factor is taken to be $r=D_1/D_{\rm ideal}=0.77857$, the answer is \b[$D_{\rm total}\simeq18.1\,\mathrm m$]. The first term is the actual 4 m, not the hypothetical loss-free distance.
This numerical inference needs the stated comparison assumption. Strictly, knowing the first actual bounce distance and saying subsequent distances share a ratio does not independently specify that ratio. A change in <spring> compression also means that an energy-loss fraction is not automatically the same as a vertical-distance ratio.
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