Indicate first 4 of the number sequence in this pattern in terms of the number of house where the street light is positioned and find the constant difference.

The problem states the positions of the first four street lights:

• The 1st street light is on the 5th house's pavement.
• The 2nd street light is on the 9th house's pavement.
• The 3rd street light is on the 13th house's pavement.
• The 4th street light is on the 17th house's pavement.

The sequence of house numbers is $5, 9, 13, 17$.
To find the constant difference, subtract consecutive terms:

The constant difference is 4.

The first 4 terms of the sequence are $\boxed{5, 9, 13, 17}$ and the constant difference is $\boxed{4}$.

The table asks for X (position of the term) and Y (constant difference by position of the term), which refers to the house number where the street light is placed.

The relationship between the position of the street light and the house number where it is placed is an arithmetic progression. Each subsequent street light is placed on a house pavement that is 4 houses further than the previous one.

This is an arithmetic sequence with the first term $a_1 = 5$ and the common difference $d = 4$.
The formula for the $n$-th term of an arithmetic sequence is $T_n = a_1 + (n-1)d$.
Substitute the values:

The formula used to position the street lights algebraically is $\boxed{T_n = 4n + 1}$.