{"id":90016,"date":"2025-06-01T10:19:11","date_gmt":"2025-06-01T10:19:11","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90016"},"modified":"2025-06-01T10:19:11","modified_gmt":"2025-06-01T10:19:11","slug":"which-one-of-the-following-is-the-wrong-number-in-the-series-6-14-30","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-wrong-number-in-the-series-6-14-30\/","title":{"rendered":"Which one of the following is the wrong number in the series 6, 14, 30"},"content":{"rendered":"

Which one of the following is the wrong number in the series 6, 14, 30, 64, 126 ?<\/p>\n

[amp_mcq option1=”126″ option2=”64″ option3=”14″ option4=”6″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is B) 64.
\n<\/section>\n
\nWe need to identify the pattern in the given series of numbers: 6, 14, 30, 64, 126.
\n<\/section>\n
\nLet the series be denoted by T(n), where n=1, 2, 3, …
\nT(1) = 6
\nT(2) = 14
\nT(3) = 30
\nT(4) = 64
\nT(5) = 126<\/p>\n

Let’s examine the relationship between consecutive terms.
\nT(2) = 14. Is there a relation to T(1)=6? 6 * 2 + 2 = 12 + 2 = 14.
\nLet’s test this pattern for the next term: T(n+1) = 2 * T(n) + 2.
\nT(3) = 2 * T(2) + 2 = 2 * 14 + 2 = 28 + 2 = 30. This matches the given T(3).
\nNow let’s test this pattern for the fourth term:
\nExpected T(4) = 2 * T(3) + 2 = 2 * 30 + 2 = 60 + 2 = 62.
\nHowever, the given fourth term is 64. This indicates that 64 might be the wrong number.<\/p>\n

Let’s assume the expected T(4) (which is 62) was correct and test the pattern for the fifth term:
\nExpected T(5) = 2 * (Expected T(4)) + 2 = 2 * 62 + 2 = 124 + 2 = 126.
\nThis matches the given T(5).<\/p>\n

So, the pattern T(n+1) = 2 * T(n) + 2 holds for all terms except for the fourth term, which should be 62 according to the pattern, but is given as 64. Therefore, 64 is the wrong number in the series.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following is the wrong number in the series 6, 14, 30, 64, 126 ? [amp_mcq option1=”126″ option2=”64″ option3=”14″ option4=”6″ correct=”option2″] This question was previously asked in UPSC CAPF – 2016 Download PDFAttempt Online The correct option is B) 64. We need to identify the pattern in the given series of numbers: … <\/p>\n

Detailed SolutionWhich one of the following is the wrong number in the series 6, 14, 30<\/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":[1098,1102],"class_list":["post-90016","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1098","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nWhich one of the following is the wrong number in the series 6, 14, 30<\/title>\n<meta name=\"description\" content=\"The correct option is B) 64. 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