{"id":4427,"date":"2021-11-24T08:23:59","date_gmt":"2021-11-24T08:23:59","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4427"},"modified":"2022-01-03T07:29:32","modified_gmt":"2022-01-03T07:29:32","slug":"consecutive-even-numbers-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/consecutive-even-numbers-with-examples-and-faqs\/","title":{"rendered":"Consecutive Even Numbers with Examples and FAQs"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Consecutive Even Numbers with Examples and FAQs<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; custom_padding=&#8221;15px|15px|54px|4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><b>What are consecutive even numbers?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Before discussing consecutive even numbers first let\u2019s start by knowing about consecutive numbers.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>Consecutive numbers<\/strong><br \/><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Numbers that follow a regular sequence or pattern are called consecutive numbers. It\u2019s a series where the difference between the numbers is fixed. The series starts from the smallest number and tends towards the largest number. For example, the set of natural numbers from 1 to 10, i.e., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, is a list of consecutive numbers where the fixed difference is \u20181\u2019 between each number.<br \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b>Consecutive Even Numbers<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Even numbers are numbers that end in either 0, 2, 4, 6 or 8. A set of even consecutive numbers is such a set where the difference between each consecutive number is \u20182\u2019. This list can be represented in the form p, p + 2, p + 4, p + 6, p + 8, \u2026 and so on. Here, p is the starting number which can be either an even integer or an even natural number.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-weight: 400;\"><strong>Properties of Even Consecutive Numbers<\/strong><br \/><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">In general, consecutive numbers follow a pattern, where the series starts from the smallest number and continues till the largest.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Following are some properties of consecutive numbers that are even:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The difference between each number of the series is fixed, and it is 2 in the case of even consecutive numbers.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The numbers in the list can only end in 0, 2, 4, 6 and 8.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The sum of all the consecutive numbers is also an even number.<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2><b>Examples<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><strong>Examples 1<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> Does the given sequence follow the properties of consecutive numbers that are even?<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/c1-300x166.png\" width=\"300\" height=\"166\" alt=\"\" class=\"wp-image-4429 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/c1-300x166.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/c1.png 304w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><strong>Solution:\u00a0<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">In the given sequence all numbers are even and the difference between each element of the series from the beginning to the end is \u20182\u2019. Hence, the given sequence is that of consecutive evens.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><strong>Example 2<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> The sum of 5 even consecutive numbers is 100. Can you identify the numbers using the concept of consecutive evens?<\/span><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">Let the first element of the series of 5 consecutive evens be \u2018a\u2019. Then the series is:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> a, (a + 2), (a + 4), (a + 6), ( a + 8).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It is given that the sum of 5 consecutive elements is 100.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore a+(a+2)+(a+4)+(a+6)+(a+8)=100 <\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow(a+a+a+a+a)+(2+4+6+8)=100 <\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow 5 a+20=100 <\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow 5 a=100-20=80 <\/span><br \/><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore a=\\frac{80}{5}=16<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Hence, the numbers are:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">16,(16+2),(16+4),(16+6),(16+8) \\Rightarrow 16,18,20,22,24<\/span>.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; 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locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Explore Other Topics<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.10.7&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#geometry\" class=\"otherc\">Geometry<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#trigonometry\" class=\"otherc\">Trigonometry<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#operations\" class=\"otherc\">Operations<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#numbers\" class=\"otherc\">Numbers<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Related Concepts<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Related Concepts<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/even-numbers-definition-properties-and-faq-mindspark\/\" class=\"otherc\">Even Numbers<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/types-of-numbers-number-system\/\" class=\"otherc\">Types of Numbers<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/composite-odd-numbers-with-examples-and-faqs\/\" class=\"otherc\">Composite Odd Numbers<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;Row for space&#8221; 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_builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; text_orientation=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"ffmanage\">\n<div class=\"textmanagestyle\">\n<div class=\"fone\">\n<p>Ready to get started ?<\/p>\n<\/div>\n<div class=\"sone\">\n<p class=\"ffbtn\"><a href=\"https:\/\/mindspark.in\/free-trial\">Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png&#8221; title_text=&#8221;down-circle&#8221; show_bottom_space=&#8221;off&#8221; align=&#8221;right&#8221; module_class=&#8221;img2&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; width=&#8221;44px&#8221; height=&#8221;18px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;FAQ Row&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|40px||40px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;FAQ&#8221; module_class=&#8221;faqstyl&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;center&#8221; header_line_height=&#8221;2.5em&#8221; background_color=&#8221;#dbedc6&#8243; max_width=&#8221;80%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_padding=&#8221;30px|25px|30px|25px|true|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Frequently Asked Questions<span style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/h1>\n<ol><\/ol>\n<h3><strong>1. What are Consecutive Even numbers?<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\"><strong>Ans: <\/strong>A set of even consecutive numbers is such a set where the difference between each consecutive number is \u20182\u2019. This list can be represented in the form p, (p + 2), (p + 4), (p + 6), (p + 8), \u2026 and so on. Here, p is the starting number which can be either an even integer or an even natural number.<\/span><\/p>\n<h3><strong>2. Is the difference between two consecutive evens always fixed?<\/strong><\/h3>\n<p><strong>Ans: <\/strong>The difference between two consecutive evens is fixed and is always 2.<strong><br \/><\/strong><\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meta Description: We can calculate the sum of the terms in a geometric progression using the formula  S = a(1-r^n)\/(1-r) when r < 1 and  S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Consecutive Even Numbers with Examples and FAQs - mydomain<\/title>\n<meta name=\"description\" content=\"Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r &lt; 1 and S = a(r^n-1)\/(r-1)when r&gt;1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/consecutive-even-numbers-with-examples-and-faqs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Consecutive Even Numbers with Examples and FAQs - 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