What is the next number in the following sequence: 28, 327, 464, 5125, ____?
Explanation
To find the next number in the sequence, we analyze the structure of each term. Each term is formed by concatenating the base number with its corresponding power.
Pattern Identification:
The sequence follows the format n(n3), where we take an integer n and concatenate it with the result of n3.
For n=2: 2(23)=28
For n=3: 3(33)=327
For n=4: 4(43)=464
For n=5: 5(53)=5125
Calculating the Next Term:
Following this pattern, for n=6, we calculate:
n=6
n3=63=216
Concatenating 6 and 216 gives us 6216.
Correct Answer: Option 1 is the correct answer.