To model the situation with an explicit formula, we can define the following variables:
- Let \( a_0 \) be the initial number of pieces of clothing the store has at the end of the first day of the month.
- Let \( d \) be the net additional pieces of clothing per day.
- Let \( n \) be the number of days after the first day, so \( n = 0 \) corresponds to the end of the first day.
The number of pieces of clothing the store has at the end of \( n \) days can be expressed as:
\[ a_n = a_0 + n \cdot d \]
This formula is explicit because it clearly calculates the total number of pieces of clothing based on the initial count and the daily net change.
Now, we want to find the number of pieces of clothing at the end of the 28th day of the month. Since day 1 corresponds to \( n = 0 \), day 28 corresponds to \( n = 27 \).
Given that \( a_{27} = 58 \), we can use the formula to write:
\[ a_{27} = a_0 + 27 \cdot d \]
Setting \( a_{27} = 58 \), we have:
\[ 58 = a_0 + 27d \]
At this point, we need either the initial number \( a_0 \) or the daily net change \( d \) to solve for the other variable. Unfortunately, without additional information about the initial quantity or the net daily change, we cannot solve for specific values for \( a_0 \) and \( d \).
In conclusion, the explicit formula for the sequence is:
\[ a_n = a_0 + n \cdot d \]
To find specific values, you would need either the initial count \( a_0 \) or the daily net change \( d \).