Permutations and Combinations

Permutations and Combinations

Question

The ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.

Answer

Let a be the first term and r be the common ratio
According to the given equation,
straight S subscript 3 over straight S subscript 6 space equals space 125 over 152 space space space space space space space rightwards double arrow space space space space space fraction numerator begin display style fraction numerator straight a left parenthesis straight r cubed minus 1 right parenthesis over denominator straight r minus 1 end fraction end style over denominator begin display style fraction numerator straight a left parenthesis straight r to the power of 6 minus 1 right parenthesis over denominator straight r minus 1 end fraction end style end fraction space equals space 125 over 152 space space space space space space space space space space space rightwards double arrow space space space space fraction numerator straight r cubed minus 1 over denominator straight r to the power of 6 minus 1 end fraction space equals space 125 over 152
rightwards double arrow space fraction numerator straight r cubed minus 1 over denominator left parenthesis straight r cubed minus 1 right parenthesis left parenthesis straight r cubed plus 1 right parenthesis end fraction space equals space 125 over 152 space space space space rightwards double arrow space space space fraction numerator 1 over denominator straight r cubed plus 1 end fraction space equals space 125 over 152 space space space space rightwards double arrow space space space space 125 straight r cubed space plus space 125 space equals space 152

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#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>

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