{"id":12888,"date":"2014-02-04T19:08:23","date_gmt":"2014-02-04T19:08:23","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=12888"},"modified":"2026-03-26T10:02:31","modified_gmt":"2026-03-26T15:02:31","slug":"arithmetic-sequence","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/arithmetic-sequence\/","title":{"rendered":"Arithmetic Sequence"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_SYOQxJbqfYI\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_SYOQxJbqfYI\" data-source-videoID=\"SYOQxJbqfYI\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Arithmetic Sequence Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Arithmetic Sequence\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_SYOQxJbqfYI:hover {cursor:pointer;} img#videoThumbnailImage_SYOQxJbqfYI {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/104-arithmetic-sequences-resized-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_SYOQxJbqfYI\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_SYOQxJbqfYI\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Arithmetic Sequence\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_SYOQxJbqfYI\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_SYOQxJbqfYI\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_SYOQxJbqfYI\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction Uzf_Function() {\n  var x = document.getElementById(\"Uzf\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"Uzf_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"Uzf\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_an_Arithmetic_Sequence\" class=\"smooth-scroll\">What is an Arithmetic Sequence?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Using_Sequences\" class=\"smooth-scroll\">Using Sequences<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Arithmetic_Sequence_Practice_Questions\" class=\"smooth-scroll\">Arithmetic Sequence Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey guys! Welcome to this video on arithmetic sequences and their formulas!<\/p>\n<p>Sequences typically have set patterns that enable us to predict what each term might be. A list of numbers ordered in a particular way is a sequence, and each individual number is referred to as a <strong>term<\/strong>.<\/p>\n<p>Understanding arithmetic sequences, and how to identify them is a great way to develop critical thinking skills. Identifying how numbers relate to each other, and what commonalities they have in a sequence can carry over into better critical thinking skills in other intellectual endeavors.<\/p>\n<h2><span id=\"What_is_an_Arithmetic_Sequence\" class=\"m-toc-anchor\"><\/span>What is an Arithmetic Sequence?<\/h2>\n<p>\nAn arithmetic sequence is a sequence or progression of numbers where the difference between each number is the same (or constant).<\/p>\n<p>For example, in the series 5, 12, 19, 26\u2026 , we can tell that this is an arithmetic sequence by subtracting each number from the one following it.<\/p>\n<div class=\"examplesentence\"><strong>Sequence:<\/strong> \\(5\\), \\(12\\), \\(19\\), \\(26\\) <br \/>\n\\(5-12 = -7\\)<br \/>\n\\(12-19 = -7\\)<br \/>\n\\(19-26 = -7\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe difference is the same each time, therefore it is a constant.<\/p>\n<h2><span id=\"Using_Sequences\" class=\"m-toc-anchor\"><\/span>Using Sequences<\/h2>\n<p>\nIn other words, to tell whether or not it is an arithmetic sequence, we need to be able to see what is happening between each number, and whatever happens between two needs to be the same thing that is happening between each consecutive number.<\/p>\n<p>Another way to write this arithmetic sequence is:<\/p>\n<div class=\"examplesentence\">\\((a, a+d, a+2d, a+3d, &#8230;)\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe letter \\(a\\) represents the first term, and the letter \\(d\\) represents the constant difference.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nSo, looking back at our sequence of numbers let\u2019s apply this. Using this method, let\u2019s plug in our numbers.<\/p>\n<p>We have \u20185\u2019 as our first term, and we know that the constant difference is 7.<\/p>\n<div class=\"examplesentence\">\\(5, 5+7, 5+2(7) , 5+3(7) \\)\\(= 5, 12, 19, 26\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhat if we wanted to find the 50th term of this sequence?<\/p>\n<p>Let\u2019s write an arithmetic sequence as a formula:<\/p>\n<div class=\"examplesentence\">\\(x_n=a+d(n-1)\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe reason \\(n &#8211; 1\\) is used is because \\(d\\), the constant difference, is not applied to the very first term.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s take a look at a new arithmetic sequence, and, using our new formula, calculate a certain term.<\/p>\n<p>Look at this sequence:<\/p>\n<div class=\"examplesentence\">\\(9, 17, 25, 33, 41, 49,\\)\\( 57, 65, 73, 81, &#8230;\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo, we are going to calculate the fourth term using our formula. We know that our first term is 9, so now we have to calculate the constant difference, which is 8.<\/p>\n<p>So we are looking for our fourth term which is represented by \\(x_4\\). \\(a\\) is our first term (which is 9), \\(d\\) is our constant difference (which is 8), and \\(n\\) represents the number&#8217;s sequence order (which in this case is 4).<\/p>\n<p>So, let\u2019s plug in our numbers.<\/p>\n<div class=\"examplesentence\">\\(x_{4} = 9 + 8(4 &#8211; 1) = 33\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, typically, you wouldn\u2019t use this formula to calculate a term that is already listed, but rather to predict and calculate a term farther along the progression of numbers.<\/p>\n<p>So, let\u2019s say we want to calculate the 1,698th term of this arithmetic sequence.<\/p>\n<div class=\"examplesentence\">\\(x_1,698 = 9 + 8(1,698-1) \\)\\(= 13,585\\)<\/div>\n<p>\n&nbsp;<br \/>\nI hope that this video was helpful!<\/p>\n<p>See you next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is arithmetic sequence?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>An arithmetic sequence is a sequence in which the same number is added or subtracted from one term to the next.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the sum of an arithmetic sequence?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>To find the sum of an arithmetic sequence, use this formula:<\/p>\n<p style=\"text-align:center;\"> \\(s_n=\\dfrac{n}{2} (a_1+a_n)\\)<\/p>\n<ul style=\"list-style-type: none\">\n<li>\\(\\:n\\): The position you are adding up to<\/li>\n<li>\\(a_1\\): The first element of the sequence<\/li>\n<li>\\(a_n\\): The element in the position you are adding up to<\/li>\n<\/ul>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the sum of the first seven elements of the sequence \\(a_n=4+(n-1) \\times 3\\)?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align:center; margin-bottom: 0em; line-height: 35px\"> \\(n=7\\)<br \/>\\(a_1=4\\)<br \/>\\(a_n=a_7\\)<br \/>\\(a7=4+(7-1) \\times 3=4+6 \\times 3\\)\\(\\:=4+18=22\\)<br \/> \\(s_7=\\frac{7}{2} (4+22)=\\frac{7}{2} (26)=91\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the nth term of an arithmetic sequence?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>To find the nth term of an arithmetic sequence, use this formula: <\/p>\n<p style=\"text-align:center;\">\\(a_n=a_1+(n-1)d\\)<\/p>\n<ul style=\"list-style-type: none\">\n<li>\\(a_n\\): The term you are looking for<\/li>\n<li>\\(a_1\\): The first term of the sequence<\/li>\n<li>\\(\\:\\:n\\): The position of the term you are looking for<\/li>\n<li>\\(\\:\\:d\\): The common difference<\/li>\n<\/ul>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the 17th term of this sequence: 1, 3, 5, 7, . . .?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align:center; margin-bottom: 0em; line-height: 35px\">\\(a_1=1\\)<br \/> \\(n=17\\)<br \/> \\(d=2\\)<br \/> \\(a_17=1+(17-1)(2)\\)\\(\\:=1+(16)(2)=1+32=33\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Arithmetic_Sequence_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Arithmetic Sequence Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the common difference in the arithmetic sequence shown below?<\/p>\n<div class=\"yellow-math-quote\">3, 10, 17, 24, 31\u2026<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">28<\/div><div class=\"PQ\"  id=\"PQ-1-2\">3<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">7<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\u20137<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>In an arithmetic sequence, the distance between each consecutive term, the common difference, is constant. In this sequence, the common difference is 7 because each term increases by 7 as the sequence progresses.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nUse the formula \\(x_n=a+d(n -1)\\) to find the 8th term in the sequence below.<\/p>\n<div class=\"yellow-math-quote\">15, 12, 9, 6\u2026<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\u20139<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">\u20136<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\u20133<\/div><div class=\"PQ\"  id=\"PQ-2-4\">3<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>In the formula, \\(n\\) represents the term we need to identify (in this case, 8), \\(a\\) represents the first term in the sequence (in this case, 15), and \\(d\\) represents the common difference (in this case, \u20133).<\/p>\n<p>Now we input our known values into our equation and solve.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(x_n=a+d(n-1)\\)<br \/>\n\\(x_8=15+(-3)(8-1)\\)<br \/>\n\\(x_8=15+(-3)(7)\\)<br \/>\n\\(x_8=15+(-21)\\)<br \/>\n\\(x_8=-6\\)<\/p>\n<p>Therefore, the 8th term in the sequence is \u20136.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nUse the formula \\(s_n=\\frac{n}{2}(a_1+a_n)\\) to find the sum of the arithmetic sequence given.<\/p>\n<div class=\"yellow-math-quote\">6, 11, 16, 21, 26<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">30<\/div><div class=\"PQ\"  id=\"PQ-3-2\">96<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">80<\/div><div class=\"PQ\"  id=\"PQ-3-4\">-50<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>In the formula, \\(n\\) represents the number of terms in the sequence (in this case, 5), \\(a_1\\) represents the first term in the sequence (in this case, 6), and \\(a_n\\) represents the last term in the sequence (in this case, 26). <\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\(s_n=\\frac{n}{2}(a_1+a_2)\\)<br \/>\n\\(s_5=\\frac{5}{2}(6+26)\\)<br \/>\n\\(s_5=\\frac{5}{2}(32)\\)<br \/>\n\\(s_5=5(16)\\)<br \/>\n\\(s_5=80\\)<\/p>\n<p>The sum of the arithmetic sequence is 80.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nDavid gets offered a new job with a starting salary of $60,000 per year. He receives an annual raise of $3,000. Based on this information, what will David\u2019s salary be in 5 years? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">$75,000 per year <\/div><div class=\"PQ\"  id=\"PQ-4-2\">$70,000 per year <\/div><div class=\"PQ\"  id=\"PQ-4-3\">$69,000 per year <\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">$72,000 per year <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Using the formula \\(x_n=a+d(n-1)\\), we can substitute the appropriate values for the variables.<\/p>\n<p>In this case, \\(n\\) represents the term we need to identify. Since we want to know David\u2019s salary in 5 years, we need to find the 5th term in this sequence. The term \\(a\\) represents the first term in the sequence, which is David\u2019s starting salary of 60,000. Finally, the term \\(d\\) represents the common difference, which is David\u2019s annual raise, 3,000.<\/p>\n<p>To solve, plug these known values into the formula and simplify.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(x_n=a+d(n-1)\\)<br \/>\n\\(x_5=60{,}000+3{,}000(5-1)\\)<br \/>\n\\(x_5=60{,}000+3{,}000(4)\\)<br \/>\n\\(x_5=60{,}000+12{,}000\\)<br \/>\n\\(x_5=72{,}000\\)<\/p>\n<p>Therefore, David will earn $72,000 per year in 5 years.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nAn auditorium has 12 rows of seats. If there are six seats in the first row, 10 in the second, 14 in the third, and so on, how many seats are there in all? Assume the pattern continues in all rows. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">336 seats<\/div><div class=\"PQ\"  id=\"PQ-5-2\">542 seats<\/div><div class=\"PQ\"  id=\"PQ-5-3\">72 seats<\/div><div class=\"PQ\"  id=\"PQ-5-4\">168 seats<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The first step is solving for the number of seats in the 12th row. Then, we can find the sum of the arithmetic sequence, which will tell the total number of seats.<\/p>\n<p>To find the number of seats in the 12th row, use the formula \\(x_n=a+d(n-1)\\) and plug in the known values of 6 for \\(a\\), 4 for \\(d\\), and 12 for \\(n\\).<\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(x_n=a+d(n-1)\\)<br \/>\n\\(x_{12}=6+4(12-1)\\)<br \/>\n\\(x_{12}=6+4(11)\\)<br \/>\n\\(x_{12}=6+44\\)<br \/>\n\\(x_{12}=50\\)<\/p>\n<p>There are 50 seats in the 12th row of the auditorium.<\/p>\n<p>Then, use the formula \\(s_n=\\frac{n}{2}(a_1+a_n)\\) to find the sum of all the seats in the auditorium. For this problem, \\(n=12\\), \\(a_1=6\\), and \\(a_n=50\\).<\/p>\n<p>Plug in these values and simplify.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\\(s_n=\\frac{n}{2}(a_1+a_n)\\)<br \/>\n\\(s_{12}=\\frac{12}{2}(6+50)\\)<br \/>\n\\(s_{12}=6(56)\\)<br \/>\n\\(s_{12}=336\\)<\/p>\n<p>Altogether, there are 336 seats in the auditorium.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/basic-arithmetic\/\">Return to Basic Arithmetic Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Basic Arithmetic Videos<\/p>\n","protected":false},"author":1,"featured_media":91105,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-12888","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-additional-topics","7":"page_category-math-advertising-group","8":"page_category-solving-equations-videos","9":"page_category-video-pages-for-study-course-sidebar-ad","10":"page_type-video","11":"content_type-practice-questions","12":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/12888","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=12888"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/12888\/revisions"}],"predecessor-version":[{"id":280118,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/12888\/revisions\/280118"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91105"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=12888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}