Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 362392 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0501 1211736 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0501 1211736 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1238 4105376 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1251 4132912 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1259 4150624 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1259 4167632 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1267 4175368 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1267 4175368 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1749 4411104 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1763 4428504 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1769 4449432 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1858 4517440 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1858 4517696 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Iterative Sequences

A sequence is a list of numbers with some rule to calculate each number in the sequence. The rule could be a formula for the nth term, for exampleor a formula which says multiply the last term by 2 and add three to get the next term,A sequence generated by a rule which uses each term to find the next term is called an iterative sequence. Usually we are given the first term, and some rule, so we can work out all succeeding terms. Sometimes it may be possible to find what is called a closed form for the nth term. The closed form is a formula for in terms of n and not in terms ofThis will mean not having to work out the first 19 terms if we want to find the 20 th term.


It might be helpful to write down the first few terms of the sequence, noting that the rule says multiply each term by 3 to get the next term:

1, 3, 9, 27, 81...

The sequence consists of all the powers of n, starting from the zeroth power,Hence we can writeThis is just an expression for terms in an arithmetic sequence.


It might be helpful to write down the first few terms of the sequence, noting that the rule says add 4 to each term to get the next term:

3, 7, 11, 15, 19......

This sequence is just an arithmetic sequence, of the formwith common difference and