Why Pb-210 is lost "as fast as" the creation through Ra-226 decay? In a material about radiometric dating, it is said that:

As fast as this background $\bf{_{}^{210}Pb}$ is lost by radioactive decay, new $\bf{_{}^{210}Pb}$ is created by the decay of $\bf{_{}^{226}Ra}$.

This sentence seems to say that the $\bf{_{}^{210}Pb}$ loss rate is the same as the creation rate, so the background $\bf{_{}^{210}Pb}$ levels in deep sediments is a constant (see black dots in picture of page 4).
But I cannot understand it: Why the two retes is the same? the half life of $\bf{_{}^{226}Ra}$ is $\mathrm{1600 yrs}$, while the half life of $\bf{_{}^{210}Pb}$ is $\mathrm{22.3 yrs}$. The loss rate of $\bf{_{}^{210}Pb}$ should be much faster than the creation rate by $\bf{_{}^{226}Ra}$ decay because of Pb-210's short half life.
 A: Given the comments under my question, now I suppose that I can solve my confusion.
It's due to the phenomenon called Secular Equilibrium:

After enough time, each intermediate decay-chain product accumulates
to an equilibrium concentration, such that the element is created at,
and decays away at, the same rate.

For example, substance $A$ and $B$ are in one decay chain. $A$ decays into $B$:
$\frac{d N_A}{d t} = -\lambda_AN_A$
$\frac{d N_B}{d t} = -\lambda_BN_B$
At secular equilibrium, the amount of $B$ does not change. Since the input of $B$ is from the decay of $A$, and the loss of $B$ is from it's own decay, it means:
$\frac{d N_A}{d t} (gain) = \frac{d N_B}{d t} (loss)$, which is: $\lambda_AN_A = \lambda_BN_B$.
I previously misunderstood this "same rate". I thought the longer half-life (smaller lambda) means smaller rate. But it is not the case, since the "rate" expressed in Secular Equilibrium means $dN/dt$ (not $\lambda$). So we cannot simply say a small lambda means a small rate. Instead, we should also take N into account (i.e., $\lambda N$).
For example, in the "Decay of uranium decay-chain products" of this blog, the decay rates for uranium-238, thorium-234,... are all the same: 12.3 kBq. It's because their quantity present are different: the equilibrium amount of each element is proportional to its half life. It means that fast-dacay matter has a low amount, slow-decay matter has a high amount.
