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Question

Which term of the A.P. $$53,48,43, \ldots$$ is the first negative term? 


Solution

From the question,
The first term $$a=53$$
Then, difference $$d=48-53=-5$$
$$=43-48=-5\\$$
Therefore, common difference $$d=-5$$
$$\begin{aligned}T_{n} &=a+(n-1) d \\&=53+(n-1)(-5) \\&=53-5 n+5 \\&=58-5 n \\5 n &=58 \\n &=58 / 5 \\n &=11.6 \approx 12\end{aligned}\\$$
Therefore, $$12^{\text {th }}$$ term is the first negative term of the A.P. $$53,48,43, \ldots$$

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