Permutations and Combinations

Permutations and Combinations

Question

Find the sum to n terms of an A.P., whose nth term is straight t subscript straight n space equals space 5 space minus space 6 straight n comma space straight n element of space straight N.

Answer

Here,            straight t subscript straight n space equals space 5 space minus space 6 straight n                                       ...(i)
Replacing n by (n - 1), we get
                   straight t subscript straight n minus 1 end subscript space equals space 5 space minus space 6 left parenthesis straight n space minus space 1 right parenthesis space equals space 5 space minus space 6 straight n space plus space 6 space equals space 11 space minus space 6 straight n   ...(ii)

∴                  d = straight t subscript straight n space minus space straight t subscript straight n minus 1 end subscript space equals space left parenthesis 5 minus 6 straight n right parenthesis space minus space left parenthesis 11 space minus space 6 straight n right parenthesis space equals space 5 space minus space 6 straight n space minus space 11 space plus space 6 straight n space equals space minus 6

which is independent of n

∴      The sequence space space open curly brackets straight t subscript straight n close curly brackets  is an A.P.
                        <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>
                        a = -1, d = -6
straight S subscript straight n space equals space straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket space equals space straight n over 2 left square bracket 2 left parenthesis negative 1 right parenthesis space plus space left parenthesis straight n minus 1 right parenthesis space left parenthesis negative 6 right parenthesis right square bracket

space space space space space space space equals space straight n over 2 left square bracket negative 2 minus 6 straight n plus 6 right square bracket space equals space straight n over 2 left square bracket 4 minus 6 straight n right square bracket space equals space straight n left parenthesis 2 minus 3 straight n right parenthesis space equals space 2 straight n space minus space 3 straight n squared
                       

More Chapters from Permutations and Combinations