Maharashtra BoardEnglish MediumSTD 10MathsArithmetic Progression3 Marks
Question
Which term of the AP $121, 117, 113, ....$ is its first negative term?
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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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