{"id":4479,"date":"2022-02-06T19:20:41","date_gmt":"2022-02-06T19:20:41","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=4479"},"modified":"2022-02-28T16:59:55","modified_gmt":"2022-02-28T16:59:55","slug":"arithmetic-sequences","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/arithmetic-sequences\/","title":{"rendered":"Arithmetic Sequences"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Arithmetic Sequences<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A progression is a sequence of numbers that follow a specific pattern. An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In an arithmetic progression, there is a possibility to derive a formula for the nth term.<\/p>\n<p>We can define an arithmetic progression in two ways:<br \/>\ni. An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.<br \/>\nii. An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]In an arithmetic sequence, each term is found by adding the same number to the previous term.<\/p>\n<p>To write an algebraic expression describing the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\">arithmetic sequence<\/a>, determine the greatest common factor between each term in the sequence.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">Write the next 3 terms in the sequence.<br \/>\n<\/span><br \/>\n5, 8, 11, 14, _____, _____, ______.<\/strong>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]1. Each term in the pattern increases by 3.<br \/>\n2. Add 3 to the last term and the next two terms.<\/p>\n<p>Answer: <span style=\"color: red;\"><strong>17, 20, 23<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Arithmetic Sequences[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write an algebraic expression to find any term in the sequence.<\/span><\/strong><br \/>\nWrite ‘n’ for the variable.<br \/>\n<strong>6, 12, 18, 24, \u2026<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><img loading=\"lazy\" class=\"alignnone wp-image-2983 size-full\" style=\"margin-top: 18px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/3-14.png\" alt=\" Arithmetic Sequences Problem 1\" width=\"109\" height=\"44\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Select the algebraic expression that could be used to find any term in the sequence.<\/span><\/strong><br \/>\n<strong>7, 11, 15, 19, __, __, __<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><img loading=\"lazy\" class=\"alignnone wp-image-4481 size-full\" style=\"margin-top: 18px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-54.png\" alt=\" Arithmetic Sequences Problem 2\" width=\"199\" height=\"122\" \/><\/a><br \/>\n<strong><span style=\"color: #16a085;\">What is the 9th term in the sequence?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><img loading=\"lazy\" class=\"alignnone wp-image-2983 size-full\" style=\"margin-top: 18px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/3-14.png\" alt=\"\" width=\"109\" height=\"44\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 15px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">The table below shows the price of apples depending on quantity. <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><img loading=\"lazy\" class=\"alignnone wp-image-4483 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/2-43.png\" alt=\" Arithmetic Sequences Problem 3\" width=\"293\" height=\"55\" \/><\/a><br \/>\n<strong><span style=\"color: #16a085;\">Select an algebraic expression that represents the given situation. <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><img loading=\"lazy\" class=\"alignnone wp-image-4485 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/3-36.png\" alt=\"\" width=\"208\" height=\"49\" \/><\/a><br \/>\n<strong><span style=\"color: #16a085;\">What is the price of 2kg of apples?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><img loading=\"lazy\" class=\"alignnone wp-image-4487 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/4-28.png\" alt=\"\" width=\"112\" height=\"34\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Algebraic Expression<\/strong> \u2013 an expression that contains variables, numbers, and at least one operation.<\/p>\n<p><strong>Term<\/strong> \u2013 each number in a sequence.<\/p>\n<p><strong>Arithmetic Sequence<\/strong> – each term is found by multiplying the same number to the previous term.<\/p>\n<p><strong>Geometric Sequence<\/strong> – each term is found by adding the same number to the previous term.<\/p>\n<p><strong>Common Difference<\/strong> \u2013 the number that a sequence is increased or decreased by.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/evaluate-algebraic-expressions\"><span style=\"color: #ed5600;\">Evaluate Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/write-algebraic-expressions\"><span style=\"color: #ed5600;\">Write Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/input-output-table-find-a-rule-1\"><span style=\"color: #ed5600;\">Input – Output Table – Find a Rule<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/input-output-table-addition-and-subtraction-1\"><span style=\"color: #ed5600;\">Input – output table – Addition and Subtraction<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/input-output-table-multiplication-and-division\"><span style=\"color: #ed5600;\">Input – Output table – Multiplication and Division<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/Number%20Patterns\"><span style=\"color: #ed5600;\">Number Patterns<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635524203859{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><span style=\"color: #333399;\"><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/geometric-sequences\"><span style=\"color: #333399;\">Geometric Sequences<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/the-distributive-property\"><span style=\"color: #333399;\">The Distributive Property<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/simplifying-complex-algebraic-expressions\"><span style=\"color: #333399;\">Simplifying Complex Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/add-linear-expressions\"><span style=\"color: #333399;\">Add Linear Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions\"><span style=\"color: #333399;\">Subtract Linear Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions\"><span style=\"color: #333399;\">Factor Linear Expressions<\/span><\/a><\/span>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” 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url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Arithmetic Sequences [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A progression is a sequence of numbers that follow a specific pattern. An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Arithmetic Sequences | Oryx Learning<\/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:\/\/oryxlearning.com\/learn\/arithmetic-sequences\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Arithmetic Sequences\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Arithmetic Sequences [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A progression is a sequence of numbers that follow a specific pattern. 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