Permutations and Combinations

Permutations and Combinations

Question

The first term of GP. is 1. The sum of 3rd and 5th term is 90. Find the common ratio of G.P.

Answer

Let a be first term and r be the common ratio of G.P.
Given a = 1,  also,  straight t subscript 3 space plus space straight t subscript 5 space equals space 90
rightwards double arrow                  ar squared space plus space ar to the power of 4 space equals space 90
rightwards double arrow          space space straight r squared plus straight r to the power of 4 space equals space 90                                                                 (∵ a = 1)
rightwards double arrow        <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>
rightwards double arrow       space space straight r to the power of 4 plus 10 straight r squared minus 9 straight r squared minus 90 space equals space 0  or straight r squared left parenthesis straight r squared plus 10 right parenthesis space minus space 9 left parenthesis straight r squared plus 10 right parenthesis space equals space 0
or       left parenthesis straight r squared minus 9 right parenthesis space left parenthesis straight r squared plus 10 right parenthesis space equals space 0
rightwards double arrow            straight r squared space minus space 9 space space equals 0                                       left parenthesis straight r squared plus 10 equals 0 space space is space impossible right parenthesis
rightwards double arrow                  straight r space equals space plus-or-minus space 3

More Chapters from Permutations and Combinations