Permutations and Combinations

Permutations and Combinations

Question

Solve the equation 1 + 6 + 11 + 16 + ........ + x = 148

Answer

The given equation is : 1 + 6 + 11 + 16 +...........+x = 148
Here, a = 1, d = 6 -1 = 5, l = x, Let x be the nth term

∴                           straight S subscript straight n space equals space 148
or           straight n over 2 left square bracket 2 straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d right square bracket space equals space 148
or           straight n over 2 left square bracket 2 left parenthesis 1 right parenthesis space plus space left parenthesis straight n space minus space 1 right parenthesis 5 right square bracket space equals space 148
or             n[2 + 5n - 5] = 296
or             n (5n - 3) = 296
or              <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>
or                  straight n equals space fraction numerator 3 plus-or-minus square root of left parenthesis 3 right parenthesis squared minus 4 left parenthesis 5 right parenthesis space left parenthesis negative 296 right parenthesis end root over denominator 2.5 space end fraction space equals space fraction numerator 3 plus-or-minus square root of 9 plus 5920 end root over denominator 10 end fraction space equals space fraction numerator 3 plus-or-minus square root of 5929 over denominator 10 end fraction space equals space fraction numerator 3 plus-or-minus 77 over denominator 10 end fraction space equals space 8 comma space space fraction numerator negative 37 over denominator 5 end fraction
rightwards double arrow                          n = 8                         (∵ n is a natural number)

∴  straight t subscript 8 space equals space straight x              or      a + (8 -1)d = x   or 1+7 (5) = x            or x = 36



More Chapters from Permutations and Combinations