Choose the correct answer in each of the following questions:

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.

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