To solve this question, we need to identify the pattern or rule that governs the sequence of numbers. Let's analyze the given sequence:
1, 2, 9, 64, 625, ?
Looking closely, we can see that each number in the sequence is obtained by raising the previous number to a certain power:
2 = 1^2
9 = 2^2
64 = 4^3
625 = 5^4
Therefore, to find the next number in the sequence, we need to raise 5 to the power of 5:
5^5 = 3125
So, the missing number in the sequence is 3125.
Now, let's go through each option to determine the correct answer:
Option A) 189 - This option is incorrect because it does not follow the pattern observed in the sequence.
Option B) 625 - This option is incorrect because it is already present in the given sequence.
Option C) 7776 - This option is incorrect because it does not follow the pattern observed in the sequence.
Option D) 149 - This option is incorrect because it does not follow the pattern observed in the sequence.
The correct answer is option C) 7776.