Correct Answer: Option D

Explanation

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

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:

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

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

\(504 = n \cdot 56\)

Now, divide both sides by 56:

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

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

There is an explanation video available below.

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