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Question:
Find the first negative term of A.P. 129,120,111,102,.........
Answer:

Given AP is:  129,120,111,102,.........

Where the first term a = 129

common difference d = 120 - 129 = -9

Let nth term is the first negative term in AP

Now nth tern in AP = a + (n-1)*d

                           = 129 + (n-1)*(-9)

                           = 129 - 9n + 9

                           = 138 - 9n

By taking value of n = 16, we get

  nth term  = 138 - 9*16

                 = 138 - 144

                 = -6

So 16th term is the first negative term of given AP 

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