**Q) **Which term of the A.P. : 65, 61, 57, 53,………… is the first negative term.

**Ans: **This is A.P. of decreasing order. In the given A.P., we can see that:

First term a = 65 and common difference d = -4

Let first negative term be n^{th} term, say T_{n}

We know that n^{th} term of an A.P. is given by T_{n }= a + (n-1) d

Since it has to be first negative term, therefore:

a + (n-1) d < 0

65 + (n-1) (-4) < 0

69 – 4n < 0

69 < 4n

n > = 17.25

Since term count has to be integer, hence, nearest integer value which is greater than 17.25 is 18.

**Therefore, 18th term of the given A.P. will be its first negative term.**

*Check:*

*Value of 17 ^{th} term will be, N_{17} = 65 + (17 – 1) (- 4) = 65 – 64 = 1*

*and value of 18 ^{th} term will be, N_{18} = 65 + (18 – 1) (- 4) = 65 – 68 = – 3, which will be the first negative term after 1.*