What is the next number in the series: 12, 15, 21, 30, 42, _?

To determine the next number in the series of 12, 15, 21, 30, 42, we first look for a pattern in the differences between consecutive numbers:

• The difference between 12 and 15 is 3.

• The difference between 15 and 21 is 6.

• The difference between 21 and 30 is 9.

• The difference between 30 and 42 is 12.

Observing these differences more closely, we see they are increasing by 3 each time: 3, 6, 9, 12. Following this pattern, the next difference should be 15 (12 + 3).

Now, if we add this next difference of 15 to the last number in the series, 42:

42 + 15 = 57.

Thus, the next number in the series is 57. This understanding of how the sequence develops through consistent increments helps clarify why 57 is the correct choice.