MCQ
Which term of the $A.P. \ \{121, 117, 113, ...\}$ is its first negative term?
- ✓$32$
- B$31$
- C$30$
- D$33$
✓
Answer
Correct option: A.
$32$
Here $, a = 121, d = 117 - 121 = -4$
for the first negative first $a_n < 0$
$\Rightarrow 121 + (n - 1) (-4) < 0$
$\Rightarrow 121 - 4n + 4 < 0$
$\Rightarrow 125 - 4n < 0$
$\Rightarrow\text{n}>\frac{125}{4}$
$\Rightarrow\text{n}>31\frac{1}{4}$
$\therefore 32^{nd}$ term is the first negative term.
for the first negative first $a_n < 0$
$\Rightarrow 121 + (n - 1) (-4) < 0$
$\Rightarrow 121 - 4n + 4 < 0$
$\Rightarrow 125 - 4n < 0$
$\Rightarrow\text{n}>\frac{125}{4}$
$\Rightarrow\text{n}>31\frac{1}{4}$
$\therefore 32^{nd}$ term is the first negative term.
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