Identifying the Term of the Progression
To find the term of the progression -1, -3, -5, ..., that is -39, we need to determine the position of -39 in the sequence.

Understanding the Arithmetic Progression
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the common difference is -2.

Finding the Position of -39
To find the position of -39 in the sequence, we can use the formula for the nth term of an arithmetic progression:
\[a_n = a_1 + (n-1)d\]
where:
- \(a_n\) is the nth term
- \(a_1\) is the first term
- \(d\) is the common difference
- \(n\) is the position of the term we are looking for
Plugging in the values we know:
- \(a_n = -39\)
- \(a_1 = -1\)
- \(d = -2\)
We can rearrange the formula to solve for \(n\):
\[-39 = -1 + (n-1)(-2)\]
Solving for \(n\):
\[-39 = -1 -2n + 2\]
\[-39 = -2n + 1\]
\[-40 = -2n\]
\[n = 20\]
Therefore, the 20th term of the progression is -39.