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The first term of an AP is (31) and (a_{19}=139). What is the common difference?किसी AP का पहला पद (31) है और (a_{19}=139) है। सार्व अंतर क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 66
For an AP, \(a_n=a+(n-1)d\). Substituting \(a=31\), \(n=19\), and \(a_{19}=139\), we get \(139=31+18d\). Thus, \(108=18d\), so \(d=6\). If the common difference were 5, the 19th term would be \(31+18\times5=121\), not 139. Exam tip: the common difference is added \(n-1\) times to reach the \(n\)th term.AP के लिए सूत्र \(a_n=a+(n-1)d\) है। यहाँ \(a=31\), \(n=19\) और \(a_{19}=139\) रखने पर \(139=31+18d\) मिलता है। अतः \(108=18d\), इसलिए \(d=6\)। विकल्प 5 लेने पर 19वाँ पद \(31+18\times5=121\) आता, जो 139 नहीं है। परीक्षा टिप: \(n\)वें पद में \(n-1\) बार सार्व अंतर जुड़ता है।
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