{"id":143429,"date":"2024-09-23T17:19:56","date_gmt":"2024-09-23T17:19:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=143429"},"modified":"2024-09-23T17:19:58","modified_gmt":"2024-09-23T17:19:58","slug":"how-many-multiples-of-3-are-there-between-100-and-1000","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/23\/how-many-multiples-of-3-are-there-between-100-and-1000\/","title":{"rendered":"How many multiples of 3 are there between 100 and 1,000"},"content":{"rendered":"\n<p>How many multiples of 3 are there between 100 and 1,000?<br>Hint: an = a1 + d(n \u2212 1), where a1 is the first term and d is the common difference.<\/p>\n\n\n\n<p>266<br>299<br>300<br>301<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find how many multiples of 3 exist between 100 and 1,000, we first determine the smallest and largest multiples of 3 within this range.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding the First Multiple of 3 Greater Than or Equal to 100:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide 100 by 3: ( \\frac{100}{3} \\approx 33.33 ).<\/li>\n\n\n\n<li>The smallest integer greater than 33.33 is 34.<\/li>\n\n\n\n<li>Thus, the first multiple of 3 is ( 3 \\times 34 = 102 ).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding the Last Multiple of 3 Less Than or Equal to 1,000:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide 1,000 by 3: ( \\frac{1000}{3} \\approx 333.33 ).<\/li>\n\n\n\n<li>The largest integer less than or equal to 333.33 is 333.<\/li>\n\n\n\n<li>Therefore, the last multiple of 3 is ( 3 \\times 333 = 999 ).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identifying the Sequence:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The multiples of 3 from 102 to 999 form an arithmetic sequence where:\n<ul class=\"wp-block-list\">\n<li>( a_1 = 102 ) (the first term),<\/li>\n\n\n\n<li>( a_n = 999 ) (the last term),<\/li>\n\n\n\n<li>( d = 3 ) (the common difference).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Using the Formula for the n-th Term:<\/strong><br>The formula for the n-th term of an arithmetic sequence is:<br>[<br>a_n = a_1 + d(n &#8211; 1)<br>]<br>Setting ( a_n = 999 ), we substitute:<br>[<br>999 = 102 + 3(n &#8211; 1)<br>]<br>Rearranging gives:<br>[<br>999 &#8211; 102 = 3(n &#8211; 1) \\<br>897 = 3(n &#8211; 1) \\<br>n &#8211; 1 = \\frac{897}{3} = 299 \\<br>n = 300<br>]<\/li>\n<\/ol>\n\n\n\n<p>Thus, there are <strong>300 multiples of 3 between 100 and 1,000<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The arithmetic sequence from 102 to 999 with a common difference of 3 yields a total of 300 terms, confirming that the answer is indeed 300. This approach showcases the use of basic arithmetic concepts and sequences to solve problems efficiently.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many multiples of 3 are there between 100 and 1,000?Hint: an = a1 + d(n \u2212 1), where a1 is the first term and d is the common difference. 266299300301 The Correct Answer and Explanation is : To find how many multiples of 3 exist between 100 and 1,000, we first determine the smallest [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-143429","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=143429"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143429\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=143429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=143429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=143429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}