How many numbers between 30 and 150 leave a remainder of 1 when divided by 5?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve this, we need to find how many numbers between 30 and 150 leave a remainder of 1 when divided by 5.<\/p>\n\n\n\n The key is to recognize that numbers which leave a remainder of 1 when divided by 5 follow a specific pattern. These numbers can be represented in the form: 5n+15n + 1<\/p>\n\n\n\n Where nn is a non-negative integer. For example, the first number in the sequence that leaves a remainder of 1 when divided by 5 is 31, since: 31\u00f75=6 remainder 131 \\div 5 = 6 \\text{ remainder } 1<\/p>\n\n\n\n The next number in the sequence is 36, which can be calculated by adding 5 to the previous number (31). The sequence continues like this: 31, 36, 41, 46, 51, …, up to the largest number less than or equal to 150.<\/p>\n\n\n\n Starting from 30, the smallest number that leaves a remainder of 1 is 31.<\/p>\n\n\n\n The largest number less than or equal to 150 that leaves a remainder of 1 is 146, because: 146\u00f75=29 remainder 1146 \\div 5 = 29 \\text{ remainder } 1<\/p>\n\n\n\n The sequence of numbers that leave a remainder of 1 when divided by 5 is: 31,36,41,46,51,\u2026,14631, 36, 41, 46, 51, \\dots, 146<\/p>\n\n\n\n This is an arithmetic sequence where the first term is 31, the common difference is 5, and the last term is 146.<\/p>\n\n\n\n To find the number of terms in this sequence, we use the formula for the nth term of an arithmetic sequence: an=a1+(n\u22121)\u22c5da_n = a_1 + (n-1) \\cdot d<\/p>\n\n\n\n Where:<\/p>\n\n\n\n Substituting these values into the formula: 146=31+(n\u22121)\u22c55146 = 31 + (n-1) \\cdot 5<\/p>\n\n\n\n Solving for nn: 146\u221231=(n\u22121)\u22c55146 – 31 = (n-1) \\cdot 5 115=(n\u22121)\u22c55115 = (n-1) \\cdot 5 n\u22121=23n-1 = 23 n=24n = 24<\/p>\n\n\n\n Thus, there are 24 numbers<\/strong> between 30 and 150 that leave a remainder of 1 when divided by 5.<\/p>\n","protected":false},"excerpt":{"rendered":" How many numbers between 30 and 150 leave a remainder of 1 when divided by 5? The correct answer and explanation is: To solve this, we need to find how many numbers between 30 and 150 leave a remainder of 1 when divided by 5. The key is to recognize that numbers which leave a […]<\/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-250406","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250406","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=250406"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250406\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Find the first number greater than or equal to 30 that leaves a remainder of 1<\/h3>\n\n\n\n
Step 2: Find the largest number less than or equal to 150 that leaves a remainder of 1<\/h3>\n\n\n\n
Step 3: Determine the total number of terms in the sequence<\/h3>\n\n\n\n
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