Permutations And Combinations

Question
CBSEENMA11012973

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

Solution

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.

∴                   straight t subscript straight n space equals space 253                 or                            l italic space italic equals italic space italic 253
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 = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>

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

 

Sponsor Area

Some More Questions From Permutations and Combinations Chapter