Which term of the A.P.: $65, 61, 57, 53, \ldots$ is the first negative term?

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Step 1: $a = 65$, $d = -4$. Let $a_n$ be the first negative term. $a_n < 0 \Rightarrow a + (n - 1)d < 0$ Step 2: $65 + (n - 1)(-4) < 0 \Rightarrow 69 - 4n < 0 \Rightarrow n > \frac{69}{4}$ Step 3: Least positive integral value of $n$ satisfying $n > \frac{69}{4}$ is $n = 18$. The $18^{ ext{th}}$ term is the first negative term of the A.P.

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