nth term = first term + (n - 1) x common difference

Sum of the series = (number of terms ) x (first term + last term)

2

0 = (__number of terms__ ) x (3 + last term)

2

last term = 3 + (n - 1) x (-1/4)

Now, substitute the expression for the last term into the sum equation:

0 = (__number of terms__ ) x (3 + 3 + (n - 1) x (-1/4))

2

Simplify the equation:

0 = (__number of terms __) x (6 - (n - 1) x (¼))

2

0 = (__number of terms __) x (24 - (n - 1))

2

0 = (__number of terms__ ) x (25 - n)

2

Case 1: Number of terms / 2 = 0

This implies that the number of terms is 0, which is not meaningful in this context.

Case 2: 25 - n = 0

Solve for n:

25 - n = 0

n = 25