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) 7th

Answer 1

The given AP is 25, 20, 15, ... .

Here, a = 25 and d = 20 − 25 = −5

Let the n^th term of the given AP be the first negative term. Then,

$$\begin{gathered} a_n<0 \\ \Rightarrow 25+\left(n-1\right)\times \left(-5\right)<0\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 30-5n<0 \\ \Rightarrow -5n<-30 \end{gathered}$$
$$\begin{gathered} \Rightarrow n>\frac{30}{5}=6 \\ \therefore n=7 \end{gathered}$$

Thus, the 7th term is the first negative term of the given AP.

Hence, the correct answer is option D.