The middle term of AP 6,13,20 ..... 216 is

1.	The middle term of AP 6,13,20 ..... 216 is
Answer» $\sf\large\underline{Given:}$ $\rm{The\: first\: term (a)=6}$ $\rm{The\:last\: term (Tn)=216}$ $\rm{The\: common\: difference=7}$ $\sf\large\underline{To\: <klux>FIND</klux>:}$ $\rm{The\: <klux>MIDDLE</klux>\: term\:of\:AP=?}$ $\sf\large\underline{Solution:}$ [At 1st calculate the number n term than calculate median (means the middle term of AP)] $\sf\large\underline{Formula\: used:}$ $\rm\purple{\implies T_{n}=a+(n-1)d}$ $\sf\large\underline{A.T.Q:}$ $\rm{\implies 216=6+(n-1)7}$ $\rm{\implies 216-6=(n-1)7}$ $\rm{\implies 210=(n-1)7}$ $\rm{\implies 30=n-1}$ $\rm{\implies n=30+1}$ $\rm\red{\implies n=31}$ [Now, CALCULATE middle term here] Total number of n term=31 $\rm{\implies M=(\dfrac{n+1}{2})th}$ $\rm{\implies M=(\dfrac{31+1}{2})th}$ $\rm{\implies M=(\dfrac{32}{2})th}$ $\rm{\implies M=16th}$ {Than find out T_16 here} $\rm{\implies T_{16}=6+(16-1)7}$ $\rm{\implies T_{16}=6+105}$ $\rm{\implies T_{16}=111}$ Hence, $\rm\red{\implies The\: middle\:term=111}$

Answer»

$\sf\large\underline{Given:}$