SOLUTION: The 5th term of an A.P is 9 and the 8th term is 27, find; the 6th term and the sum of the 7th and 11th term

?,?,?,?,9,?,?,27,?,?,?, ...

Let d be the common difference between every two terms. Then,

Then the 6th term is the 5th term plus d and
the 7th term is the 8th term minus d:

?,?,?,?,9,9+d,27-d,27,?,?,?, ...

When you add d to the 6th term, you get the 7th term, so,

(9+d) + d = (27-d)

9 + d + d = 27 - d
   9 + 2d = 27 - d
       3d = 18
        d = 6 

?,?,?,?,9,9+6,27-6,27,?,?,?, ...

?,?,?,?,9,15,21,27,?,?,?, ...
   
Now just add 6 over and over to get the terms on the right
and subtract 6 over and over to get the terms on the left:

-5,-9,-3,3,9,15,21,27,33,39,45,51, 

Now you can finish.

Edwin