Question:
Choose the correct answer in each of the following questions:
Which term of the AP 25, 20, 15, ... is the first negative term?
(a) 10th
(b) 9th
(c) 8th
(d) 7 th
Solution:
The given AP is 25, 20, 15, ... .
Here, a = 25 and d = 20 − 25 = −5
Let the nth term of the given AP be the first negative term. Then,
$a_{n}<0$
$\Rightarrow 25+(n-1) \times(-5)<0 \quad\left[a_{n}=a+(n-1) d\right]$
$\Rightarrow 30-5 n<0$
$\Rightarrow-5 n<-30$
$\Rightarrow n>\frac{30}{5}=6$
$\therefore n=7$
Thus, the 7th term is the first negative term of the given AP.
Hence, the correct answer is option D.