Answer :
This sequence seems to involve power relations of some kind. Let's look at the numbers and analyze their pattern:
The first term is [tex]1[/tex], which is [tex]1^n[/tex], where [tex]n = 0[/tex].
The second term is [tex]4[/tex], which can be written as [tex]2^2[/tex].
The third term is [tex]27[/tex], which is [tex]3^3[/tex].
The term before last is [tex]3125[/tex], which is [tex]5^5[/tex].
The missing term is the fourth one in this sequence.
If we observe the pattern, we can see that the number and the power are the same (a number raised to itself yields the result in the series). Let's establish a process to find the missing term:
- From the sequence: [tex]1^1, 2^2, 3^3, \text{?}, 5^5[/tex].
- Clearly, the fourth term should be [tex]4^4[/tex].
Calculating [tex]4^4[/tex]:
[tex]4^4 = 4 \times 4 \times 4 \times 4 = 256[/tex]
So, the missing term in the sequence is [tex]256[/tex].
Therefore, the correct option is C. 256.
