{"id":8890,"date":"2023-04-30T10:00:03","date_gmt":"2023-04-30T04:30:03","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=8890"},"modified":"2023-05-01T09:40:17","modified_gmt":"2023-05-01T04:10:17","slug":"sequences","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/sequences\/","title":{"rendered":"Sequences"},"content":{"rendered":"<h2><span style=\"color: #3366ff;\"><strong>Sequences<\/strong><\/span><\/h2>\n<p>In the previous lesson, we learned about <a href=\"https:\/\/www.aplustopper.com\/what-is-the-pattern-of-numbers\/\">pattern of numbers<\/a>. In this lesson we discuss about\u00a0Sequences.<\/p>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7EmWdysUk0c?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>A sequence is an ordered list of numbers.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12953\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/12\/sequences-1.jpg\" alt=\"\" width=\"546\" height=\"238\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/12\/sequences-1.jpg 546w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/12\/sequences-1-300x131.jpg 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\nThe sum of the terms of a sequence is called a <strong>series<\/strong>.<\/p>\n<ul>\n<li>Each number of a sequence is called a term (or element) of the sequence.<\/li>\n<li>A finite sequence contains a finite number of terms (you can count them). 1, 4, 7, 10, 13<\/li>\n<li>An infinite sequence contains an infinite number of terms (you cannot count them). 1, 4, 7, 10, 13, . . .<\/li>\n<li>The terms of a sequence are referred to in the subscripted form shown below, where the natural number subscript refers to the location (position) of the term in the sequence.<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128462\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-1.jpg\" alt=\"Sequences 1\" width=\"305\" height=\"55\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-1.jpg 305w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-1-300x54.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/li>\n<\/ul>\n<p>(If you study computer programming languages such as C, C++, and Java,<br \/>\nyou will find that the first position in their arrays (sequences) start with a subscript of zero.)<\/p>\n<p>The general form of a sequence is represented:<\/p>\n<ul>\n<li>The domain of a sequence consists of the counting numbers 1, 2, 3, 4, &#8230; and the range consists of the terms of the sequence.<\/li>\n<li>The terms in a sequence may, or may not, have a pattern, or a related formula.<\/li>\n<li>For some sequences, the terms are simply random.<\/li>\n<\/ul>\n<p>Let&#8217;s examine some sequences that have patterns:<\/p>\n<p>Sequences often possess a definite pattern that is used to arrive at the sequence&#8217;s terms.<\/p>\n<p>It is often possible to express such patterns as a formula. In the sequence shown at the left, an explicit formula may be:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128464\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-2.jpg\" alt=\"Sequences 2\" width=\"329\" height=\"139\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-2.jpg 329w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-2-300x127.jpg 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p><strong>Examples<\/strong>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128465\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-3.jpg\" alt=\"Sequences 3\" width=\"607\" height=\"200\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-3.jpg 607w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-3-300x99.jpg 300w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128466\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-4.jpg\" alt=\"Sequences 4\" width=\"592\" height=\"218\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-4.jpg 592w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-4-300x110.jpg 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128470\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-5.jpg\" alt=\"Sequences 5\" width=\"589\" height=\"213\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-5.jpg 589w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-5-300x108.jpg 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128471\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-6.jpg\" alt=\"Sequences 6\" width=\"599\" height=\"198\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-6.jpg 599w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/Sequences-6-300x99.jpg 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p><a class=\"button-red\" title=\"Maths\" href=\"https:\/\/www.aplustopper.com\/maths\/\">Maths<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sequences In the previous lesson, we learned about pattern of numbers. In this lesson we discuss about\u00a0Sequences. A sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. Each number of a sequence is called a term (or element) of the sequence. A finite sequence contains [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[55912,55948,3246],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sequences - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/sequences\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sequences\" \/>\n<meta property=\"og:description\" content=\"Sequences In the previous lesson, we learned about pattern of numbers. 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