In a A.P., the first term is 2 and the sum of first five terms is one-fourth of the sum of the next five terms. Show that the 20th term is – 112.

Here, a = 2, Let d be the common difference. Since the sum of first five terms is one-fourth of the sum of the next five terms.

or                                  or                      or        
or                     
or                      or                  50 + 50d = 20 + 45d
or                  5d = -30                             or                             d = -6
Now,                                           
                           = 2 + 19 (-6) = 2 - 114 = -112