Which term of the AP 121, 117, 113, … is its first negative term?
Question:

Which term of the AP 121, 117, 113, … is its first negative term?

Solution:

The given AP is 121, 117, 113, … .

Here, a = 121 and d = 117 − 121 = −4

Let the nth term of the given AP be the first negative term. Then,

$a_{n}<0$

$\Rightarrow 121+(n-1) \times(-4)<0 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow 125-4 n<0$

$\Rightarrow-4 n<-125$

$\Rightarrow n>\frac{125}{4}=31 \frac{1}{4}$

$\therefore n=32$

Hence, the 32nd term is the first negative term of the given AP.