If are in A.P., prove that are in A.P. from Mathematics Seque

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 Multiple Choice QuestionsShort Answer Type

51.

If <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> are in A.P. prove that a, b, c are in A.P.

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52.

If a, b, c are in A.P., prove that fraction numerator 1 over denominator square root of straight b plus square root of straight c end fraction comma space fraction numerator 1 over denominator square root of straight c plus square root of straight a end fraction comma space fraction numerator 1 over denominator square root of straight a plus square root of straight b space end root end fraction are also in A.P.

90 Views

53.

If straight a squared comma space straight b squared comma space straight c squared are in A.P., then prove that fraction numerator straight a over denominator straight b plus straight c end fraction comma space fraction numerator straight b over denominator straight c plus straight a end fraction comma space fraction numerator straight c over denominator straight a plus straight b end fraction are in A.P.

83 Views

54.

If <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> are in A.P., show that fraction numerator 1 over denominator straight b minus straight c end fraction comma space fraction numerator 1 over denominator straight c minus straight a end fraction comma space fraction numerator 1 over denominator straight a minus straight b end fraction are in A.P.

104 Views

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55.

If space space left parenthesis straight b minus straight c right parenthesis squared comma space left parenthesis straight c minus straight a right parenthesis squared comma space left parenthesis straight a minus straight b right parenthesis squared are in A.P., prove that fraction numerator 1 over denominator straight b minus straight c end fraction comma space fraction numerator 1 over denominator straight c minus straight a end fraction comma space fraction numerator 1 over denominator straight a minus straight b end fraction are in A.P.


Since space left parenthesis straight b minus straight c right parenthesis squared comma space left parenthesis straight c minus straight a right parenthesis squared comma space left parenthesis straight a minus straight b right parenthesis squared are in A.P.

∴  space space space left parenthesis straight c minus straight a right parenthesis squared minus space left parenthesis straight b minus straight c right parenthesis squared space equals space left parenthesis straight a minus straight b right parenthesis squared minus left parenthesis straight c minus straight a right parenthesis squared

or    left parenthesis straight c minus straight a plus straight b minus straight c right parenthesis left parenthesis straight c minus straight a minus straight b plus straight c right parenthesis space equals space left parenthesis straight a minus straight b plus straight c minus straight a right parenthesis left parenthesis straight a minus straight b minus straight c plus straight a right parenthesis

or     (b - a) (2c - a - b) = (c - b) (2a - b - c)                                  ...(i)

Now, fraction numerator 1 over denominator straight b minus straight c end fraction comma space fraction numerator 1 over denominator straight c minus straight a end fraction comma space fraction numerator 1 over denominator straight a minus straight b end fraction will be in A.P.

if         space space space space fraction numerator 1 over denominator straight c minus straight a end fraction minus fraction numerator 1 over denominator straight b minus straight c end fraction space equals space fraction numerator 1 over denominator straight a minus straight b end fraction minus fraction numerator 1 over denominator straight c minus straight a end fraction or if  fraction numerator straight b minus straight c minus straight c plus straight a over denominator left parenthesis straight c minus straight a right parenthesis space left parenthesis straight b minus straight c right parenthesis end fraction = fraction numerator straight c minus straight a minus straight a plus straight b over denominator left parenthesis straight a minus straight b right parenthesis left parenthesis straight c minus straight a right parenthesis end fraction

or if          <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>                              (Note this step carefully)

or if (b - a) (2c - a - b) = (c - b) (2a - b - c) which is true.                [By using (i)]

Hence, space space fraction numerator 1 over denominator straight b minus straight c end fraction comma space space fraction numerator 1 over denominator straight c minus straight a end fraction comma space fraction numerator 1 over denominator straight a minus straight b end fraction are in A.P.

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56.

If a, b, c are in A.P. then prove that left parenthesis straight a minus straight c right parenthesis squared space equals space 4 left parenthesis straight b squared minus ac right parenthesis

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57.

If a, b, c are in A.P. then prove that

straight a cubed plus 4 straight b cubed plus straight c cubed space equals space 3 straight b left parenthesis straight a squared plus straight c squared right parenthesis

81 Views

58.

For what values of x, the numbers <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> are in G.P.?

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59.

Find the 10th term of the series 5 + 25 + 125 + ....... . Also, find its wth term.

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60.

which term of the series:

space space 1 minus 1 half plus 1 fourth minus 1 over 8 plus........ space is space minus 1 over 128

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