Find the odd one out.

The correct option is 5 : 25 : 125.

Step-by-step Explanation:

To find the odd one out, let us analyze the relationship between the numbers in each set.

Let the numbers in a set be represented as $a:b:c$.

Let us examine the pattern followed by the options:

Option 1: 4 : 16 : 256

$b=4^2=16$

$c={16}^2=256$

Here, the second number is the square of the first number, and the third number is the square of the second number.

Option 2: 3 : 9 : 81

$b=3^2=9$

$c=9^2=81$

This set follows the exact same pattern.

Option 4: 6 : 36 : 1296

$b=6^2=36$

$c={36}^2=1296$

This set also follows the exact same pattern.

Option 3: 5 : 25 : 125

$b=5^2=25$

However, for the third term:

${25}^2=625\ne 125$

Instead, $125=5^3$. Thus, this option deviates from the pattern shared by the other three options.

Therefore, 5 : 25 : 125 is the odd one out.