Explanation:

Let’s break this down:

- The given set is (9, 15, 27).

? 9 is 3², 27 is 3³, and 15 is right in between (the arithmetic mean of 9 and 27 is 18, not 15, so that's not it).

? Look for a pattern.

? 15 - 9 = 6, 27 - 15 = 12. So, the differences double each time.

Now, let's look at the options:

- (6, 9, 18):

? 9 - 6 = 3, 18 - 9 = 9. Not the same pattern.

- (15, 25, 35):

? 25 - 15 = 10, 35 - 25 = 10. Differences are equal, not doubling.

- (21, 35, 56):

? 35 - 21 = 14, 56 - 35 = 21. No clear doubling or same pattern.

- (12, 20, 36):

? 20 - 12 = 8, 36 - 20 = 16. Here, the difference doubles (8, then 16).

The correct answer is clearly option 4: (12, 20, 36)

- In both the given set and option 4, the difference between numbers increases by a factor of two. That’s the key relationship.

- The other options either have equal differences or non-doubling, mismatched steps.

So, you nailed it.