The sum of first 4 terms of an A.P. is 56. The sum of last 4 terms is 112. If its first term is 11, then find the number of terms.

Let a be first term, d be common difference, l be the last term of A.P.
Given                                  a = 11, 
                                    
            22 + 3d = 28 3d = 6 d = 2.
Also, Sum of last 4 terms = 112
l + (l -d) + (l - 2d) + (l - 3d) = 112
                   41 - 6d = 112   
Let 31 be the nth term.

∴                              
or               11 + (n - 1) 2 = 31           or    (n - 1)2 = 20         or   n - 1 = 10     or    n = 11.