Permutations and Combinations

Permutations and Combinations

Question

If the GP.’s 5,10, 20, .......and 1280, 640, 320, ......have their nth terms equal, find the value of n.

Answer

The first G.P. is : 5, 10, 20,...........
Here, a = 5, straight r space equals space 10 over 5 space equals space 2
                nth term = <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>
The second G.P. is: 1280, 640, 320, ...........
Here, a = 1280,  straight r equals 640 over 1280 space equals space 1 half
nth term = ar to the power of straight n minus 1 end exponent space equals space 1280 open parentheses 1 half close parentheses to the power of straight n minus 1 end exponent
Since the nth terms of both the G.P.'s are equal

∴      5 left parenthesis 2 right parenthesis to the power of straight n minus 1 end exponent space equals space 1280 open parentheses 1 half close parentheses to the power of straight n minus 1 end exponent space space space space space space rightwards double arrow space space space 2 to the power of straight n minus 1 end exponent space equals space 256 over 2 to the power of straight n minus 1 end exponent space space space space rightwards double arrow space space space 2 to the power of straight n minus 1 end exponent. space 2 to the power of straight n minus 1 end exponent space equals space 2 to the power of 8
rightwards double arrow           2 to the power of 2 straight n minus 2 end exponent space equals space 2 to the power of 8 space space space rightwards double arrow space space 2 straight n space minus space 2 space equals space 8 space space space rightwards double arrow space space 2 straight n space equals space 10 space space rightwards double arrow space space straight n space equals space 5

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