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What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?

A. 67 B. 45 C. -30 D. -48 Answer: Option C
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Solution(By Apex Team)

$\begin{aligned}&T_3=a+2d=-13\ldots\ldots\text{ (1) }\\ &T_6=a+5d=-4\ldots\text{ (2) }\\ &\text{ on solving (1) and }\\ &d=3\&a=-19\\ &S_n=\frac{n}{2}[2a+(n-1)d]\\ &S_{12}=\frac{12}{2}[2(-19)+(12-1)(3)]\\ &S_{12}=(6)[-38+33]\\ &S_{12}=-30\end{aligned}$

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