{"id":42523,"date":"2024-04-15T21:10:55","date_gmt":"2024-04-15T21:10:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=42523"},"modified":"2024-04-15T21:10:55","modified_gmt":"2024-04-15T21:10:55","slug":"find-the-missing-term-4-9-9-20-39-86","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/find-the-missing-term-4-9-9-20-39-86\/","title":{"rendered":"Find the missing term: 4\/9, 9\/20, ? , 39\/86"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a988ae031fed\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    17\/40                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    19\/42                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    20\/45                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    29\/53                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The answer is $\\boxed{\\frac{29}{53}}$.<\/p>\n<p>The sequence is a geometric sequence with a common ratio of $\\frac{2}{3}$. This means that each term is $\\frac{2}{3}$ times the term before it.<\/p>\n<p>The first term is $\\frac{4}{9}$. The second term is $\\frac{4}{9} \\times \\frac{2}{3} = \\frac{9}{20}$. The third term is $\\frac{9}{20} \\times \\frac{2}{3} = \\frac{18}{30}$. The fourth term is $\\frac{18}{30} \\times \\frac{2}{3} = \\frac{29}{53}$.<\/p>\n<p>Here is a table of the terms of the sequence:<\/p>\n<p>Term | Value<br \/>\n&#8212;&#8212;- | &#8212;&#8212;&#8211;<br \/>\n1 | $\\frac{4}{9}$<br \/>\n2 | $\\frac{9}{20}$<br \/>\n3 | $\\frac{18}{30}$<br \/>\n4 | $\\frac{29}{53}$<\/p>\n<p>Here is a graph of the sequence:<\/p>\n<p>[asy]<br \/>\nunitsize(1 cm);<\/p>\n<p>real ticklen = 1;<br \/>\nreal tickspace = 1;<br \/>\nreal axisarrowsize = 0.14inch;<br \/>\nreal tickdown = -0.5;<br \/>\nreal tickdownlength <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> = -0.12inch;<br \/>\nreal tickdownbase = -0.25inch;<br \/>\nreal wholetickdown = tickdown;<br \/>\nreal wholetickdownlength = tickdownlength;<br \/>\nreal wholetickdownbase = tickdownbase;<br \/>\nreal axiswidth = 0.12inch;<br \/>\nreal linetype = 1;<br \/>\nreal linewidth = 0.7pt;<br \/>\nreal dotsep = 3pt;<br \/>\nreal dotsize = 3pt;<\/p>\n<p>real g = 1.2;<\/p>\n<p>real ticklength = 0.14inch;<br \/>\nreal axismargin = 0.1inch;<br \/>\nreal xmargin = 1.2inch;<br \/>\nreal ymargin = 1.2inch;<\/p>\n<p>draw((0,-1.2)&#8211;(0,1.2),Arrows(0.14inch));<br \/>\ndraw((-1.2,0)&#8211;(1.2,0),Arrows(0.14inch));<\/p>\n<p>label(&#8220;$x$&#8221;,(1.2,0),SE);<br \/>\nlabel(&#8220;$y$&#8221;,(0,1.2),NW);<\/p>\n<p>real i;<br \/>\nfor (i=-1; i&lt;=1; ++i) {<br \/>\n <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>  draw((i,-0.1)&#8211;(i,0.1));<br \/>\n}<\/p>\n<p>real j;<br \/>\nfor (j=-1; j&lt;=1; ++j) {<br \/>\n  draw((0,j)&#8211;(0.1,j));<br \/>\n}<\/p>\n<p>real t;<br \/>\nfor (t=0; t&lt;=1; t+=0.1) {<br \/>\n  draw((t,-0.05)&#8211;(t,0.05));<br \/>\n}<\/p>\n<p>real x;<br \/>\nreal y;<\/p>\n<p>x = 0;<br \/>\ny = 4\/9;<br \/>\ndraw((x,y)&#8211;(x+0.1,y),linetype,linewidth);<\/p>\n<p>x = 0;<br \/>\ny = 9\/20;<br \/>\ndraw((x,y)&#8211;(x+0.1,y),linetype,linewidth);<\/p>\n<p>x = 0;<br \/>\ny = 18\/30;<br \/>\ndraw((x,y)&#8211;(x+0.1,y),linetype,linewidth);<\/p>\n<p>x = 0;<br \/>\ny = 29\/53;<br \/>\ndraw((x,y)&#8211;(x+0.1,y),linetype,linewidth);<\/p>\n<p>label(&#8220;$\\frac{4}{9}$&#8221;,(-0.1,4\/9),SE);<br \/>\nlabel(&#8220;$\\frac{9}{20}$&#8221;,(-0.1,9\/20),SE);<br \/>\nlabel(&#8220;$\\frac{18}{30}$&#8221;,(-0.1,18\/30),SE);<br \/>\nlabel(&#8220;$\\frac{29}{53}$&#8221;,(-0.1,29\/53),SE);<br \/>\n[\/asy]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[717],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Find the missing term: 4\/9, 9\/20, ? 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