CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Which term of the $AP. 53, 48, 43,...$ is the first negative term?
✓
Answer
Given AP is $53,48,43, \ldots \ldots$
Whose, first term $(a)=53$ and common difference $(d)=48-53=-5$ Let $n ^{\text {th }}$ term of the AP be the first negative term.
$\left[\because n^{\text {th }} \text { term an AP, } T_n=a+(n-1) d\right]$
$i.e., T_n< 0$
${a + (n - 1)d} < 0$
$\Rightarrow 53 + (n - 1)(-5) < 0$
$\Rightarrow 53 - 5n + 5 < 0$
$\Rightarrow 58 - 5n < 0$
$\Rightarrow 5n > 58$
$\Rightarrow n > 11.6$
$\Rightarrow n = 12$
i.e., $12^{th}$ term is the first negative term of the given AP.
$\therefore$ $T_{12} = a + (12 - 1)d$
$\Rightarrow T_{12} = 53 + 11(-5)$
$\Rightarrow T_{12} = 53 - 55$
$\Rightarrow T_{12} = -2 < 0$
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