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The sum of $n$ terms of an arithmetic progression is $\;n\;(2n-1)$. What is the $m^{th}$ term of the series?

$(a)\;m\;(2m-1)\qquad(b)\;2m-1\qquad(c)\;4m-3\qquad(d)\;4m+1$

Can you answer this question?

Answer : (c) 4m-3
Explanation : $T_{m}=S_{m}-S_{m-1}=m\;(2m-1)-(m-1)\;[2(m-1)-1]$
$=2m^2-m-\;(2m^2-5m+3)$
$=4m-3.$
answered Jan 18, 2014 by