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.
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