{"id":90190,"date":"2025-06-01T10:22:35","date_gmt":"2025-06-01T10:22:35","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90190"},"modified":"2025-06-01T10:22:35","modified_gmt":"2025-06-01T10:22:35","slug":"the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/","title":{"rendered":"The average of 7 consecutive odd numbers is M. If the next 3 odd numbe"},"content":{"rendered":"

The average of 7 consecutive odd numbers is M. If the next 3 odd numbers are also included, the average<\/p>\n

[amp_mcq option1=”remains unchanged” option2=”increases by 1.5″ option3=”increases by 2″ option4=”increases by 3″ correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet the 7 consecutive odd numbers be represented by an arithmetic progression with a common difference of 2. Let the middle term (4th term) be M, since for an odd number of terms in an AP, the average is the middle term. The 7 numbers are $M-6, M-4, M-2, M, M+2, M+4, M+6$. Their average is M.
\nThe next 3 consecutive odd numbers after M+6 are $M+8, M+10, M+12$.
\nThe new set of numbers consists of the original 7 plus these 3, totaling 10 numbers: $M-6, M-4, M-2, M, M+2, M+4, M+6, M+8, M+10, M+12$.
\nTo find the new average, we sum these 10 numbers and divide by 10.
\nSum of the first 7 numbers is $7M$.
\nSum of the next 3 numbers is $(M+8) + (M+10) + (M+12) = 3M + 30$.
\nTotal sum of the 10 numbers = $7M + (3M + 30) = 10M + 30$.
\nNew average = $(10M + 30) \/ 10 = M + 3$.
\nThe original average was M. The new average is M+3. The increase in average is $(M+3) – M = 3$.
\n<\/section>\n
\nWhen adding consecutive terms to an arithmetic progression, the average shifts. Adding terms that are all greater than the current average increases the average.
\n<\/section>\n
\nFor any arithmetic progression, adding $k$ terms immediately following the last term of a sequence of $n$ terms will result in a new sequence of $n+k$ terms. The increase in average depends on $n$, $k$, and the common difference $d$. In this case, the common difference is 2. Adding $k=3$ terms after $n=7$ terms, the average increases by $(k \\times d \/ 2) \\times (n \/ (n+k))$ related term? No, simpler calculation method is better. The average of the $n$ numbers is $A_n$. The average of the $n+k$ numbers $A_{n+k}$ is $\\frac{n A_n + \\text{Sum of } k \\text{ terms}}{n+k}$. The $k$ terms are $a_{n+1}, \\ldots, a_{n+k}$. The average of the $n$ terms is $a_1 + (n-1)d\/2$. The average of the $k$ new terms is $a_{n+1} + (k-1)d\/2$. This method is more complex than the one used in the primary explanation using M as the middle term. The increase of 3 is consistent.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The average of 7 consecutive odd numbers is M. If the next 3 odd numbers are also included, the average [amp_mcq option1=”remains unchanged” option2=”increases by 1.5″ option3=”increases by 2″ option4=”increases by 3″ correct=”option4″] This question was previously asked in UPSC CAPF – 2017 Download PDFAttempt Online Let the 7 consecutive odd numbers be represented by … <\/p>\n

Detailed SolutionThe average of 7 consecutive odd numbers is M. If the next 3 odd numbe<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1101,1102],"class_list":["post-90190","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1101","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe average of 7 consecutive odd numbers is M. If the next 3 odd numbe<\/title>\n<meta name=\"description\" content=\"Let the 7 consecutive odd numbers be represented by an arithmetic progression with a common difference of 2. Let the middle term (4th term) be M, since for an odd number of terms in an AP, the average is the middle term. The 7 numbers are $M-6, M-4, M-2, M, M+2, M+4, M+6$. Their average is M. The next 3 consecutive odd numbers after M+6 are $M+8, M+10, M+12$. The new set of numbers consists of the original 7 plus these 3, totaling 10 numbers: $M-6, M-4, M-2, M, M+2, M+4, M+6, M+8, M+10, M+12$. To find the new average, we sum these 10 numbers and divide by 10. Sum of the first 7 numbers is $7M$. Sum of the next 3 numbers is $(M+8) + (M+10) + (M+12) = 3M + 30$. Total sum of the 10 numbers = $7M + (3M + 30) = 10M + 30$. New average = $(10M + 30) \/ 10 = M + 3$. The original average was M. The new average is M+3. The increase in average is $(M+3) - M = 3$. When adding consecutive terms to an arithmetic progression, the average shifts. Adding terms that are all greater than the current average increases the average.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The average of 7 consecutive odd numbers is M. If the next 3 odd numbe\" \/>\n<meta property=\"og:description\" content=\"Let the 7 consecutive odd numbers be represented by an arithmetic progression with a common difference of 2. Let the middle term (4th term) be M, since for an odd number of terms in an AP, the average is the middle term. The 7 numbers are $M-6, M-4, M-2, M, M+2, M+4, M+6$. Their average is M. The next 3 consecutive odd numbers after M+6 are $M+8, M+10, M+12$. The new set of numbers consists of the original 7 plus these 3, totaling 10 numbers: $M-6, M-4, M-2, M, M+2, M+4, M+6, M+8, M+10, M+12$. To find the new average, we sum these 10 numbers and divide by 10. Sum of the first 7 numbers is $7M$. Sum of the next 3 numbers is $(M+8) + (M+10) + (M+12) = 3M + 30$. Total sum of the 10 numbers = $7M + (3M + 30) = 10M + 30$. New average = $(10M + 30) \/ 10 = M + 3$. The original average was M. The new average is M+3. The increase in average is $(M+3) - M = 3$. When adding consecutive terms to an arithmetic progression, the average shifts. Adding terms that are all greater than the current average increases the average.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:22:35+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The average of 7 consecutive odd numbers is M. If the next 3 odd numbe","description":"Let the 7 consecutive odd numbers be represented by an arithmetic progression with a common difference of 2. Let the middle term (4th term) be M, since for an odd number of terms in an AP, the average is the middle term. The 7 numbers are $M-6, M-4, M-2, M, M+2, M+4, M+6$. Their average is M. The next 3 consecutive odd numbers after M+6 are $M+8, M+10, M+12$. The new set of numbers consists of the original 7 plus these 3, totaling 10 numbers: $M-6, M-4, M-2, M, M+2, M+4, M+6, M+8, M+10, M+12$. To find the new average, we sum these 10 numbers and divide by 10. Sum of the first 7 numbers is $7M$. Sum of the next 3 numbers is $(M+8) + (M+10) + (M+12) = 3M + 30$. Total sum of the 10 numbers = $7M + (3M + 30) = 10M + 30$. New average = $(10M + 30) \/ 10 = M + 3$. The original average was M. The new average is M+3. The increase in average is $(M+3) - M = 3$. When adding consecutive terms to an arithmetic progression, the average shifts. Adding terms that are all greater than the current average increases the average.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/","og_locale":"en_US","og_type":"article","og_title":"The average of 7 consecutive odd numbers is M. If the next 3 odd numbe","og_description":"Let the 7 consecutive odd numbers be represented by an arithmetic progression with a common difference of 2. Let the middle term (4th term) be M, since for an odd number of terms in an AP, the average is the middle term. The 7 numbers are $M-6, M-4, M-2, M, M+2, M+4, M+6$. Their average is M. The next 3 consecutive odd numbers after M+6 are $M+8, M+10, M+12$. The new set of numbers consists of the original 7 plus these 3, totaling 10 numbers: $M-6, M-4, M-2, M, M+2, M+4, M+6, M+8, M+10, M+12$. To find the new average, we sum these 10 numbers and divide by 10. Sum of the first 7 numbers is $7M$. Sum of the next 3 numbers is $(M+8) + (M+10) + (M+12) = 3M + 30$. Total sum of the 10 numbers = $7M + (3M + 30) = 10M + 30$. New average = $(10M + 30) \/ 10 = M + 3$. The original average was M. The new average is M+3. The increase in average is $(M+3) - M = 3$. When adding consecutive terms to an arithmetic progression, the average shifts. Adding terms that are all greater than the current average increases the average.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:22:35+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/","name":"The average of 7 consecutive odd numbers is M. If the next 3 odd numbe","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:22:35+00:00","dateModified":"2025-06-01T10:22:35+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the 7 consecutive odd numbers be represented by an arithmetic progression with a common difference of 2. Let the middle term (4th term) be M, since for an odd number of terms in an AP, the average is the middle term. The 7 numbers are $M-6, M-4, M-2, M, M+2, M+4, M+6$. Their average is M. The next 3 consecutive odd numbers after M+6 are $M+8, M+10, M+12$. The new set of numbers consists of the original 7 plus these 3, totaling 10 numbers: $M-6, M-4, M-2, M, M+2, M+4, M+6, M+8, M+10, M+12$. To find the new average, we sum these 10 numbers and divide by 10. Sum of the first 7 numbers is $7M$. Sum of the next 3 numbers is $(M+8) + (M+10) + (M+12) = 3M + 30$. Total sum of the 10 numbers = $7M + (3M + 30) = 10M + 30$. New average = $(10M + 30) \/ 10 = M + 3$. The original average was M. The new average is M+3. The increase in average is $(M+3) - M = 3$. When adding consecutive terms to an arithmetic progression, the average shifts. Adding terms that are all greater than the current average increases the average.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-7-consecutive-odd-numbers-is-m-if-the-next-3-odd-numbe\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"The average of 7 consecutive odd numbers is M. 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