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.

Solution

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 = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
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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Permutations And Combinations

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

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