Final answer:
The sequence in question seems to follow a pattern of inverting the digits and dividing by a decreasing factor. Since the division factor reduces by 1 each step, after inverting 36 to 63 and dividing by 1, the next number in the sequence should be 63.
Step-by-step explanation:
The sequence 18, 81, 27, 72, 36, 63 seems to follow a pattern where each number is inverted and then divided or multiplied by a certain factor to get the next number. To identify the pattern, let's look at how we move from one number to the next:
- 18 (invert) -> 81 (divide by 3) -> 27
- 27 (invert) -> 72 (divide by 2) -> 36
- 36 (invert) -> 63 (divide by ...?)
Observing the pattern, the factor of division decreases by 1 each time. Since 81 was divided by 3 and 72 was divided by 2, it follows that 63 should be divided by 1, which would yield 63 since any number divided by 1 is the number itself. Therefore, the next number in the sequence is 63.