The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

A. 50th B. 502th C. 508th D. None of these Answer: Option D
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Solution(By Apex Team)

$\begin{array}{l}\begin{aligned}a_n&=a+(n-1)d\\ a_9&=449\\ &=a+(9-1)d\\ &=a+8d\ldots\ldots(1)\\ a_{449}&=9\\ &=a+(449-1)d\\ &=a+448d\ldots(2)\end{aligned}\\ \text{ Subtracting }\\ 440d=-440\\ \begin{array}{l}\Rightarrow d=\frac{-440}{440}=-1\\ \text{ and }a+8d=449\\ \Rightarrow a\times8\times(-1)=449\\ \Rightarrow a=449+8=457\\ \therefore0=a+(n-1)d\\ \Rightarrow0=457+(n-1)(-1)\\ \Rightarrow0=457-n+1\\ \Rightarrow n=458\\ \therefore458^{\text{th }}\text{ term }=0\end{array}\end{array}$

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