Select the number from among the given options that can replace the question mark (?) in the following series.
$$20,21,25,34,?,75$$

Let us find the difference between consecutive terms of the series:$21-20=1=1^2$$25-21=4=2^2$$34-25=9=3^2$ The differences are consecutive perfect squares ($1^2,2^2,3^2,\dots$).Following this logic, the next difference should be $4^2=16$.Therefore, the missing number is:
$$34+16=50$$
Let's verify with the next term:
$$50+5^2=50+25=75$$
This matches the final term perfectly.