Write the first five terms of each of the sequences whose nth te
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    The Fibonacci sequence is defined by
                       <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>
    Find fraction numerator straight a subscript straight n plus 1 over denominator straight a subscript straight n end fraction, for n = 1, 2, 3, 4, 5.

    The Fibonacci sequence is given by

                                  straight a subscript 1 space equals space straight a subscript 2 space equals space 1

    and                          straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript plus straight a subscript straight n minus 2 end subscript

    Putting n =3 in (i), we get straight a subscript 3 space equals space straight a subscript 3 minus 1 end subscript space plus space straight a subscript 3 minus 2 end subscript space equals space straight a subscript 2 space plus space straight a subscript 1 space equals space 1 space plus space 1 space equals space 2

    Putting n = 4 in (i), we get straight a subscript 4 space equals space straight a subscript 4 minus 1 end subscript space plus space straight a subscript 4 minus 2 end subscript space equals space straight a subscript 3 plus straight a subscript 2 space equals space 2 space plus space 1 space equals 3

    Putting n = 5 in (i), we get straight a subscript 5 equals straight a subscript 5 minus 1 end subscript plus straight a subscript 5 minus 2 end subscript equals straight a subscript 4 plus straight a subscript 3 equals 3 plus 2 equals 5

    Putting n = 6 in (i), we get straight a subscript 6 space equals space straight a subscript 6 minus 1 end subscript space plus space straight a subscript 6 minus 2 end subscript space equals space straight a subscript 5 plus straight a subscript 4 space equals space 5 space plus space 3 space equals 8

    Now, let       straight t subscript straight n space equals space straight a subscript straight n plus 1 end subscript over straight a subscript straight n

                      straight t subscript 1 space equals space fraction numerator straight a subscript 1 plus 1 over denominator straight a subscript 1 end fraction space equals space fraction numerator straight a subscript 2 over denominator straight a subscript 1 space end fraction space equals space 1 over 1 space equals space 1 commastraight t subscript 2 space equals space fraction numerator straight a subscript 2 plus 1 over denominator straight a subscript 2 end fraction space equals space straight a subscript 3 over straight a subscript 2 space equals space 2 over 1 equals 2 comma space space space straight t subscript 3 space equals space fraction numerator straight a subscript 3 plus 1 over denominator straight a subscript 3 end fraction space equals space straight a subscript 4 over straight a subscript 3 equals space 3 over 2

                     straight t subscript 4 space equals space fraction numerator straight a subscript 4 plus 1 over denominator straight a subscript 4 end fraction space equals space straight a subscript 5 over straight a subscript 4 space equals space 5 over 3 comma space space straight t subscript 5 space equals space fraction numerator straight a subscript 5 plus 1 over denominator straight a subscript 5 end fraction space equals space straight a subscript 6 over straight a subscript 5 space equals space 8 over 5

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    Write the first five terms of each of the sequences whose nth terms are :
    straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n squared plus 5 right parenthesis over denominator 4 end fraction

    Here straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n squared plus 5 right parenthesis over denominator 4 end fraction

    Putting n = 1, 2, 3, 4, 5, we get

            space space straight a subscript 1 space equals space fraction numerator 1 left parenthesis 1 squared plus 5 right parenthesis over denominator 4 end fraction space equals space 6 over 4 space equals space 3 over 2 comma space space space straight a subscript 2 space equals space fraction numerator 2 left parenthesis 2 squared plus 5 right parenthesis over denominator 4 end fraction space equals space 9 over 2 comma space space straight a subscript 3 space equals space fraction numerator 3 left parenthesis 3 squared plus 5 right parenthesis over denominator 4 end fraction space equals space 21 over 2

              straight a subscript 4 equals space fraction numerator 4 left parenthesis 4 squared plus 5 right parenthesis over denominator 4 end fraction equals 21 comma space space space straight a subscript 5 equals space fraction numerator 5 left parenthesis 5 squared plus 5 right parenthesis over denominator 4 end fraction space equals space 75 over 2

    ∴ First five terms are 3 over 2 comma space space 9 over 2 comma space 21 over 2 comma space 21 comma space 75 over 2

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    Write first five terms of the following sequence and obtain the corresponding series.
    <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> for all n>1

    Here, <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>

    Now,               straight a subscript straight n space equals space 3 straight a subscript straight n minus 1 end subscript space plus space 2                               ...(i)  (for n>1)

    Putting  n = 2 in (i), we get straight a subscript 2 space equals space 3 straight a subscript 1 space plus space 2 space equals space 3 space left parenthesis 3 right parenthesis space plus space 2 space equals space 9 space plus space 2 space equals space 11

    Putting n = 3 in (i), we get straight a subscript 3 space equals space 3 straight a subscript 2 space plus space 2 space equals space 3 space left parenthesis 11 right parenthesis space plus space 2 space equals space 33 space plus space 2 space equals space 35

    Putting n =4 in (i), we get straight a subscript 4 space equals space 3 straight a subscript 3 space plus space 2 space equals space 3 space left parenthesis 35 right parenthesis space plus space 2 space equals space 105 space plus space 2 space equals space 107

    Putting n = 5 in (i), we get straight a subscript 5 equals space 3 straight a subscript 4 plus space 2 space equals space 3 space left parenthesis 107 right parenthesis space plus space 2 space equals space 321 space plus space 2 space equals space 323.

    The corresponding series is : 3 + 11 + 35 + 107 + 323 + ..........

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    Answer

    Write the first five terms of the sequence whose nth terms are:
    straight a subscript straight n space equals space left parenthesis negative 1 right parenthesis to the power of straight n minus 1 end exponent space 5 to the power of straight n plus 1 end exponent



    Here, straight a subscript straight n space equals space left parenthesis negative 1 right parenthesis to the power of straight n minus 1 end exponent 5 to the power of straight n plus 1 end exponent

    Putting n = 1, 2, 3, 4, 5, we get

                           <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>

                           straight a subscript 2 space equals space left parenthesis negative 1 right parenthesis to the power of 2 minus 1 end exponent 5 to the power of 2 plus 1 end exponent equals negative 5 cubed equals negative 125

                           straight a subscript 3 space equals space left parenthesis negative 1 right parenthesis to the power of 3 minus 1 end exponent 5 to the power of 3 plus 1 end exponent space equals space 5 to the power of 4 space equals space 625 straight a subscript 4 space equals space left parenthesis negative 1 right parenthesis to the power of 4 minus 1 end exponent 5 to the power of 4 plus 1 end exponent equals space minus 5 to the power of 5 space equals space minus 3125 straight a subscript 5 space equals space left parenthesis negative 1 right parenthesis to the power of 5 minus 1 end exponent 5 to the power of 5 plus 1 end exponent equals space 5 to the power of 6 space equals space 15625

    ∴   First five terms are: 25, -125, 625, -3125, 15625


                           
                          
           
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    Answer

    Write first five terms of the following sequence and obtain the corresponding series.
    straight a subscript 1 space equals space straight a subscript 2 space equals space 2 comma space space space straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript space minus space 1, n>2

    Here,        space straight a subscript 1 space equals space 2 comma space space space straight a subscript 2 equals 2.

                    space space space straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript minus 1                        ...(i) (for n>2)


    Putting n = 3 in (i), we get straight a subscript 3 equals straight a subscript 2 minus 1 space equals space 2 space minus space 1 space equals 1.

    Putting n = 4 in (i), we get straight a subscript 4 space equals space straight a subscript 3 minus 1 space equals space 1 space minus space 1 space equals 0

    Putting n = 5 in (i), we get <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 corresponding series is: 2 + 2 + 1 + 0 - 1 ...............

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