Question

Find the sum of all the $11$ terms of an $A.P.$ whose middle term is $30$.

Answer 1

Let the numbers be

$(a-5d),(a-4d),(a-3d),(a-2d),(a-d),a,(a+d),(a+2d),(a+3d),(a+4d),(a+5d).Then,$

Middle Term=$6^{th}$ term$=a=30$.

Now, Sum=$(a-5d)+(a-4d)+(a-3d)+(a-2d)+(a-d)+a+(a+d)+(a+2d)+(a+3d)+(a+4d)+(a+5d)=11a$

$\therefore Sum=11\times 30=330$