With respect to different number system bases, each number in the sequence 10000, 121, 100, 31, 24, P. 20 represents the same decimal number x. The missing number P in this sequence is:

Correct option is A

This problem is about converting the same number from various number systems (with different bases) to its decimal equivalent.
Let’s break it down:
· 10000 (base 2) = 1 × 2^4 = 16
· 121 (base 3) = 1 × 3^2 + 2 × 3 + 1 = 9 + 6 + 1 = 16
· 100 (base 4) = 1 × 4^2 = 16
· 31 (base 5) = 3 × 5 + 1 = 15 + 1 = 16
· 24 (base 6) = 2 × 6 + 4 = 12 + 4 = 16
· P (base 7) should be equal to 16. Thus, P = 22 in base 7 (2 × 7 + 2 = 16).
Therefore, P = 22 (base 7).
Information Booster:
1. The decimal equivalent of the same number in different number systems is calculated by summing the weighted positions.
2. In each base, the number must convert back to the same decimal number, 16 in this case.
Additional Knowledge:
Base systems range from binary (base 2) to base 10 (decimal) and beyond. Base conversions are a common operation in computer science.