Which number should come next in the series, 48, 24, 12, ?
The next number in the series would be 6. 

The pattern in this series is that each number is half of the previous number. 

Starting with 48, dividing by 2 gives 24. Dividing 24 by 2 gives12. Therefore, dividing 12 by 2 gives 6, which is the next number in the series.
Good. Now try this one: 18, 24, 42, ?
The next number in this series could be **66** using similar logic to the Fibonacci sequence.

In the Fibonacci sequence, the next term in the series is equal to the sum of the two past terms.

In the series you provided, 42 is equal to the sum of the two previous terms, i.e. 18 + 24 = 42. Therefore, using the same logic, to find the next term, we add the two terms behind this new term, 24 and 42. 24 + 42 = 66, so 66 is the next number in this series.