{"id":93424,"date":"2025-06-01T11:50:15","date_gmt":"2025-06-01T11:50:15","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93424"},"modified":"2025-06-01T11:50:15","modified_gmt":"2025-06-01T11:50:15","slug":"the-average-of-seven-consecutive-natural-numbers-is-13-if-the-next-th","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-seven-consecutive-natural-numbers-is-13-if-the-next-th\/","title":{"rendered":"The average of seven consecutive natural numbers is 13. If the next th"},"content":{"rendered":"

The average of seven consecutive natural numbers is 13. If the next three consecutive natural numbers are also included, the new average will be<\/p>\n

[amp_mcq option1=”15.0″ option2=”14.5″ option3=”13.5″ option4=”13.0″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is 14.5.
\n<\/section>\n
\nThe average of seven consecutive natural numbers is given as 13.
\nIn an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term.
\nFor 7 consecutive numbers, the middle term is the 4th number.
\nSo, the 4th number is 13.
\nLet the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$.
\n$n+3 = 13 \\implies n = 10$.
\nThe seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16.
\nThe sum of these 7 numbers is $7 \\times 13 = 91$.
\nThe next three consecutive natural numbers are 17, 18, 19.
\nWhen these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers.
\nThe sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers.
\nSum of next 3 numbers = 17 + 18 + 19 = 54.
\nTotal sum of 10 numbers = 91 + 54 = 145.
\nThe new average = Total sum \/ Number of terms = 145 \/ 10 = 14.5.
\n<\/section>\n
\nFor any series of consecutive numbers (or any arithmetic progression), adding new terms that are consecutive to the series will shift the average. If ‘k’ consecutive terms are added to an arithmetic progression with common difference ‘d’, the new average will be the original average plus $(k \\times d)\/2$. In this case, 3 consecutive natural numbers (d=1) were added to the original 7 numbers. The increase in average is $(3 \\times 1)\/2 = 1.5$. New average = Original average + Increase = 13 + 1.5 = 14.5. This shortcut works specifically because the numbers are consecutive and added sequentially to the original list.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The average of seven consecutive natural numbers is 13. If the next three consecutive natural numbers are also included, the new average will be [amp_mcq option1=”15.0″ option2=”14.5″ option3=”13.5″ option4=”13.0″ correct=”option2″] This question was previously asked in UPSC CISF-AC-EXE – 2024 Download PDFAttempt Online The correct answer is 14.5. The average of seven consecutive natural numbers … <\/p>\n

Detailed SolutionThe average of seven consecutive natural numbers is 13. If the next th<\/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":[1089],"tags":[1103,1102],"class_list":["post-93424","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1103","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe average of seven consecutive natural numbers is 13. If the next th<\/title>\n<meta name=\"description\" content=\"The correct answer is 14.5. The average of seven consecutive natural numbers is given as 13. In an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term. For 7 consecutive numbers, the middle term is the 4th number. So, the 4th number is 13. Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$. $n+3 = 13 implies n = 10$. The seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16. The sum of these 7 numbers is $7 times 13 = 91$. The next three consecutive natural numbers are 17, 18, 19. When these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers. The sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers. Sum of next 3 numbers = 17 + 18 + 19 = 54. Total sum of 10 numbers = 91 + 54 = 145. The new average = Total sum \/ Number of terms = 145 \/ 10 = 14.5.\" \/>\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-seven-consecutive-natural-numbers-is-13-if-the-next-th\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The average of seven consecutive natural numbers is 13. If the next th\" \/>\n<meta property=\"og:description\" content=\"The correct answer is 14.5. The average of seven consecutive natural numbers is given as 13. In an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term. For 7 consecutive numbers, the middle term is the 4th number. So, the 4th number is 13. Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$. $n+3 = 13 implies n = 10$. The seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16. The sum of these 7 numbers is $7 times 13 = 91$. The next three consecutive natural numbers are 17, 18, 19. When these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers. The sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers. Sum of next 3 numbers = 17 + 18 + 19 = 54. Total sum of 10 numbers = 91 + 54 = 145. The new average = Total sum \/ Number of terms = 145 \/ 10 = 14.5.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-seven-consecutive-natural-numbers-is-13-if-the-next-th\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:50:15+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The average of seven consecutive natural numbers is 13. If the next th","description":"The correct answer is 14.5. The average of seven consecutive natural numbers is given as 13. In an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term. For 7 consecutive numbers, the middle term is the 4th number. So, the 4th number is 13. Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$. $n+3 = 13 implies n = 10$. The seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16. The sum of these 7 numbers is $7 times 13 = 91$. The next three consecutive natural numbers are 17, 18, 19. When these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers. The sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers. Sum of next 3 numbers = 17 + 18 + 19 = 54. Total sum of 10 numbers = 91 + 54 = 145. The new average = Total sum \/ Number of terms = 145 \/ 10 = 14.5.","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-seven-consecutive-natural-numbers-is-13-if-the-next-th\/","og_locale":"en_US","og_type":"article","og_title":"The average of seven consecutive natural numbers is 13. If the next th","og_description":"The correct answer is 14.5. The average of seven consecutive natural numbers is given as 13. In an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term. For 7 consecutive numbers, the middle term is the 4th number. So, the 4th number is 13. Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$. $n+3 = 13 implies n = 10$. The seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16. The sum of these 7 numbers is $7 times 13 = 91$. The next three consecutive natural numbers are 17, 18, 19. When these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers. The sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers. Sum of next 3 numbers = 17 + 18 + 19 = 54. Total sum of 10 numbers = 91 + 54 = 145. The new average = Total sum \/ Number of terms = 145 \/ 10 = 14.5.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-seven-consecutive-natural-numbers-is-13-if-the-next-th\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:50:15+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-seven-consecutive-natural-numbers-is-13-if-the-next-th\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-average-of-seven-consecutive-natural-numbers-is-13-if-the-next-th\/","name":"The average of seven consecutive natural numbers is 13. If the next th","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:50:15+00:00","dateModified":"2025-06-01T11:50:15+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is 14.5. The average of seven consecutive natural numbers is given as 13. In an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term. For 7 consecutive numbers, the middle term is the 4th number. So, the 4th number is 13. Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$. $n+3 = 13 \\implies n = 10$. The seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16. The sum of these 7 numbers is $7 \\times 13 = 91$. The next three consecutive natural numbers are 17, 18, 19. When these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers. The sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers. Sum of next 3 numbers = 17 + 18 + 19 = 54. Total sum of 10 numbers = 91 + 54 = 145. 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