Question

find the middle term of the AP 6,13,20.............,216

Answer 1

a=6; d=13-6=7
l=a+(n-1)d=216
6+(n-1)×7=216
7 (n-1)=210
(n-1)=30
n=31
middle term=31/2=15.5
so iF the middle term is 16th term
then,
16th term=a+15d=6+15×7=6+105=111

I guess its the answer...
Hope it's helpful

Answer 2

Given AP is 6,13,20.......216
  We have find middle term
         
     First find total no. of term in this AP.
     
        for this, a= 6, d= 7 & an=216

     so, 216= a + (n-1)d = 6 + (n-1)7  
           216= 6 + 7n - 7 
           216= 7n-1
       So, n= 217/7= 31
       So there are 31 terms in A.P.
       so, middle term is 16th term.

 so, middle term, a16= a+ 15d
                                    = 6+15(7)
                                    = 6+105
                                    = 111
 so ,middle term of given AP is 111