The sum of first m terms of an A.P. is 4m2 − m.


The sum of first $m$ terms of an A.P. is $4 m^{2}-m$. If its nth term is 107 . find the value of $n$. Also, find the 21 st term of this A.P.


$S_{m}=4 m^{2}-m$

We know


$\therefore a_{m}=4 m^{2}-m-4(m-1)^{2}+(m-1)$

$a_{m}=8 m-5$



$\Rightarrow 8 n-5=107$

$\Rightarrow 8 n=112$

$\Rightarrow n=14$


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