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an arithmetic series has common difference as -1/4 and first term as 3 .find the number of terms that would give a sum of 0

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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

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