Question
Which term of the A.P. $105, 101, 97 …$ is the first negative term?

Answer

Here $a = 105$ and $d = 101 - 105 = -4$
Let $a_n$ be the first negative term.
$\Rightarrow a_n < 0$
$\Rightarrow a + (n - 1)d < 0$
$\Rightarrow 105 + (n - 1)(-4)<0$
$\Rightarrow 105 - 4n + 4 <0$
$\Rightarrow 109 - 4n < 0$
$\Rightarrow 109 <4n$
$\Rightarrow 27.25 < n$
The value of $n = 28$.
Therefore $28^{th}$ term is the first negative term of the given A.P.

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