Determine the number of terms in an A.P. 3, 8, 13, .......253. Also, find 12th term from the end.

The given A.P. is : 3, 8, 13, ....., 253
Here, a = 3, d = 8 - 3 = 5
Let there be n terms of an A.P.

∴                                    or                           
or            a + (n - 1)d = 253            or                 3 + (n - 1) 5 = 253
or             3 + 5n - 5 = 253              or                       5n - 2 = 253
or                  5n = 255                   or                             n = 51
Since nth term from end =

∴    12th term from end = 253 - (12 - 1)5 = 253 - (11) (5) = 253 - 55 = 198