CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Which term of the AP 121, 117, 113, .... is its first negative term?
✓
Answer
The given AP is 121, 117, 113, ...,
Common difference = 117 - 121 = -4
The general term of an AP is given by
$a_n = a + (n - 1)d$
$\Rightarrow a + (n - 1)d < 0$
$\Rightarrow 121 + (n - 1)(-4) <0$
$\Rightarrow 121 - 4n + 4 <0$
$\Rightarrow -4n + 125 <0$
$\Rightarrow -4n < - 125$
$\Rightarrow\text{n}>\frac{125}{4}=31.25$
So, n > 31.25
Hence, the first negative term would be the $32^{nd}$ term.
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