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Permutations And Combinations

Question
CBSEENMA11012971

Which term of the sequence space space 24 comma space 23 1 fourth comma space 22 1 half comma space 21 3 over 4 comma space space..... is the first negative term?

Solution

The given sequence <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> is an A.P. with a = 24, straight d equals 23 1 fourth minus 24 space equals space minus 3 over 4
Let the nth term of the given A.P. be the first negative term.
Then,             straight T subscript straight n space equals space straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d space less than 0.
or            24 + (n - 1) open parentheses negative 3 over 4 close parentheses space less than space 0          or      96 - 3n + 3 < 0
or                         99 - 3n < 0                or                3n > 99
or                                  n > 33
Since 34 is the natural number just greater than 33.

∴  n = 34, Hence, 34th term of the given A.P. is the first negative term.

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