Here first term a=53 and common difference d=−5

Let nth term is the first negative term of the given AP.

Therefore,

nth term in AP = a + (n – 1)*d

= 53 + (n -1)*(- 5)

= 53 – 5n + 5

= 53 + 5 – 5n

= 58 – 5n

Now, we have to find the suitable value of n, so that the value of (58 – 5n) is negative.

Let us take n = 11

nth term = 58 – (5*11)

= 58 – 55

= 3 Which is not negative.

Then putting n = 12, we get.

nth term = 58 – (5*12)

= 58 – 60

= – 2

This is the first negative term of the series, and it is the 12th term of the AP.

So, n =12