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Answer :
To find the next number in the sequence 1, 4, 27, 256, we need to identify a pattern or rule that the numbers follow. Let's look at each number:
The number 1 can be expressed as [tex]1^1[/tex].
The number 4 can be expressed as [tex]2^2[/tex].
The number 27 can be expressed as [tex]3^3[/tex].
The number 256 can be expressed as [tex]4^4[/tex].
Looking at these, we can observe that each number is of the form [tex]n^n[/tex], where [tex]n[/tex] represents the position in the sequence:
- For the first number (1st position), [tex]n = 1[/tex], and we have [tex]1^1[/tex].
- For the second number (2nd position), [tex]n = 2[/tex], and we have [tex]2^2[/tex].
- For the third number (3rd position), [tex]n = 3[/tex], and we have [tex]3^3[/tex].
- For the fourth number (4th position), [tex]n = 4[/tex], and we have [tex]4^4[/tex].
Following this pattern, the next number should be [tex]5^5[/tex].
Calculating that gives us:
[tex]5^5 = 3125[/tex]
Therefore, the next number in the sequence is 3125.
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