{"id":228036,"date":"2025-06-06T18:53:06","date_gmt":"2025-06-06T18:53:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228036"},"modified":"2025-06-06T18:53:09","modified_gmt":"2025-06-06T18:53:09","slug":"identify-next-three-numbers-in-this-sequence-2-6-3-9-6-18-15","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/identify-next-three-numbers-in-this-sequence-2-6-3-9-6-18-15\/","title":{"rendered":"Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15"},"content":{"rendered":"\n<p>Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15<br>Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Sequence Given:<\/strong><\/h3>\n\n\n\n<p>2, 6, 3, 9, 6, 18, 15<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Next Three Numbers:<\/strong><\/h3>\n\n\n\n<p><strong>45, 36, 108<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation <\/strong><\/h3>\n\n\n\n<p>To identify the next numbers in a sequence, we look for patterns\u2014either arithmetic, geometric, alternating, or a combination. Let&#8217;s examine the given sequence:<\/p>\n\n\n\n<p><strong>2, 6, 3, 9, 6, 18, 15<\/strong><\/p>\n\n\n\n<p>Split the sequence into <strong>two interleaved patterns<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Odd positions (1st, 3rd, 5th, 7th):<\/strong><br>2, 3, 6, 15<\/li>\n\n\n\n<li><strong>Even positions (2nd, 4th, 6th):<\/strong><br>6, 9, 18<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Pattern in Odd Positions (2, 3, 6, 15):<\/strong><\/h4>\n\n\n\n<p>We observe the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 \u2192 3: +1<\/li>\n\n\n\n<li>3 \u2192 6: \u00d72<\/li>\n\n\n\n<li>6 \u2192 15: \u00d72.5<\/li>\n<\/ul>\n\n\n\n<p>So it alternates between <strong>+1, \u00d72, \u00d72.5&#8230;<\/strong><\/p>\n\n\n\n<p>Let\u2019s continue this pattern:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>15 \u2192 next: +3.5 = <strong>18.5<\/strong>? That seems inconsistent.<br>Wait\u2014let\u2019s try another idea:<\/li>\n<\/ul>\n\n\n\n<p>Look again:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 \u2192 3: \u00d71.5<\/li>\n\n\n\n<li>3 \u2192 6: \u00d72<\/li>\n\n\n\n<li>6 \u2192 15: \u00d72.5<\/li>\n<\/ul>\n\n\n\n<p>This is a better fit: each term is multiplied by increasing 0.5 steps.<\/p>\n\n\n\n<p>If this is correct:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>15 \u00d7 3 = <strong>45<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So the next in this subsequence is <strong>45<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Pattern in Even Positions (6, 9, 18):<\/strong><\/h4>\n\n\n\n<p>Let\u2019s look at how these numbers behave:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 \u2192 9: +3 or \u00d71.5<\/li>\n\n\n\n<li>9 \u2192 18: \u00d72<\/li>\n<\/ul>\n\n\n\n<p>Try multiplication:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 \u00d7 1.5 = 9<\/li>\n\n\n\n<li>9 \u00d7 2 = 18<br>So the multipliers are increasing: \u00d71.5, \u00d72<\/li>\n<\/ul>\n\n\n\n<p>Continue:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>18 \u00d7 2.5 = <strong>45<\/strong><\/li>\n<\/ul>\n\n\n\n<p>That\u2019s interesting\u2014same number as before! But wait, this is only the 6th term.<\/p>\n\n\n\n<p>So the pattern continues:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Even position after 18 \u2192 <strong>18 \u00d7 2.5 = 45<\/strong><\/li>\n\n\n\n<li>Next even: 45 \u00d7 3 = <strong>135<\/strong><\/li>\n<\/ul>\n\n\n\n<p>But since we alternate, the sequence goes:<br>Odd: 2, 3, 6, 15, <strong>45<\/strong><br>Even: 6, 9, 18, <strong>54<\/strong>, <strong>108<\/strong><\/p>\n\n\n\n<p>So final combined sequence:<\/p>\n\n\n\n<p>2, 6, 3, 9, 6, 18, 15, <strong>45, 36, 108<\/strong><\/p>\n\n\n\n<p>Answer: <strong>45, 36, 108<\/strong><br>Note: 36 is from 18 \u00d7 2 (next even position term).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-573.jpeg\" alt=\"\" class=\"wp-image-228037\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15 The Correct Answer and Explanation is: Sequence Given: 2, 6, 3, 9, 6, 18, 15 Next Three Numbers: 45, 36, 108 Explanation To identify the next numbers in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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