Calculate the Average of the Sequence: 21, 0, 0, 0

To solve this problem, we'll follow these steps to find the average:

• Step 1: Calculate the sum of the given numbers.
• Step 2: Determine the total number of numbers provided.
• Step 3: Use the formula for the average to find the solution.

Now, let's work through each step:
Step 1: Sum the numbers given: $21 + 0 + 0 + 0 = 21$.
Step 2: Count the total number of numbers: There are $4$ numbers in total.
Step 3: Calculate the average using the formula:
$\text{Average} = \frac{\text{Sum of numbers}}{\text{Total number of numbers}} = \frac{21}{4} = 5.25$

This can be written as a mixed number: $5\frac{1}{4}$.

Thus, the solution to the problem is $5\frac{1}{4}$, corresponding to choice 4.