\( 78 \cdot F = \{ 5,12,19,26,33,40 , \ldots \} \)

This sequence we've been given is actually an arithmetic sequence where each term increases by 7. The first term is 5, and if we look closely, the nth term can be represented by the formula \( a_n = 5 + 7(n-1) \). This means each number can be traced back to its position as an increment of 7 from the initial value. To resolve \( 78 \cdot F \) to form this sequence, you can simply express \( F \) as the sequence divided by 78. So, to find \( F \), we need to identify the values of \( n \) and expand the equation, leading to \( F = \frac{5 + 7(n-1)}{78} \) for any value of \( n \). A little algebra can easily show how this connects with your sequence!