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Which term of the A.P. : $65, 61, 57, 53, \dots$ is the first negative term ?
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Sol. $65, 61, 57, 53, \dots$
$a = 65, d = -4$
Let $a_n$ be the first negative term
$a_n < 0 \Rightarrow a+(n-1)d < 0$
$65 + (n - 1) (-4) <0 \Rightarrow 69 – 4n < 0$
$n > \frac{69}{4}$
$\therefore$ Least positive integral value of $n$ which satisfies $n > \frac{69}{4}$ is $18$
$\therefore 1^{st}$ negative term of the AP = $18$
$a = 65, d = -4$
Let $a_n$ be the first negative term
$a_n < 0 \Rightarrow a+(n-1)d < 0$
$65 + (n - 1) (-4) <0 \Rightarrow 69 – 4n < 0$
$n > \frac{69}{4}$
$\therefore$ Least positive integral value of $n$ which satisfies $n > \frac{69}{4}$ is $18$
$\therefore 1^{st}$ negative term of the AP = $18$