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Which term of the AP: 53, 48, 43,... is the first negative term?

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$\text{The given AP: } 53, 48, 43, \ldots \\ a = 53 \\ d = 48 - 43 = -5 \\ \text{We know that the negative term is less than 0.} \\ \text{Let } n\textsuperscript{th} \text{ term be the negative term.} \\ a_{n} < 0 \\ a + (n - 1) \times d < 0 \quad (\text{using } a_{n} = a + (n-1)d) \\ 53 + (n - 1) \times (-5) < 0 \\ (n - 1) \times (-5) < -53 \\ -5n + 5 < -53 \\ -5n < -58 \\ 5n > 58 \\ \text{Hence, the } 12\textsuperscript{th} \text{ term is the first negative term.}$

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