To find the number of terms \(n\) in the arithmetic progression (AP), we use the formula for the sum of the first \(n\) terms of an AP:

\(S_n = \frac{n}{2} (a + l)\)

where:
- \(S_n\) is the sum of the first \(n\) terms,
- \(a\) is the first term,
- \(l\) is the last term.

Given:
- \(S_n = 252\)
- \(a = -16\)
- \(l = 72\)

Step 1: Substitute the Known Values

Substituting the values into the sum formula:

\(252 = \frac{n}{2} (-16 + 72)\)

Step 2: Simplify the Equation

Calculate \(-16 + 72\):

\(-16 + 72 = 56\)

Now substitute this back into the equation:

\(252 = \frac{n}{2} \cdot 56\)

Step 3: Solve for \(n\)

Multiply both sides by 2 to eliminate the fraction:

\(504 = n \cdot 56\)

Now, divide both sides by 56:

\(n = \frac{504}{56}\) = 9

Thus, the number of terms in the series is: 9