Select the missing number from the following options to complete the given series:
$$60,90,180,450,1350,\_\_\_\_\_,18900,85050,425250$$

Let's look at the multiplication pattern between consecutive terms of the series:
* $60\times 1.5=90$
* $90\times 2=180$
* $180\times 2.5=450$
* $450\times 3=1350$

The multiplying factor increases by $0.5$ at each step. Following this pattern, the next multiplier must be $3.5$:

$$\text{Missing number}=1350\times 3.5=4725$$

Let's check the subsequent terms to verify:

* $4725\times 4=18900$
* $18900\times 4.5=85050$
* $85050\times 5=425250$

The pattern is perfectly consistent. The missing number is $4725$.