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If the first term of an AP is (22) and (a_{32}=177), what is the common difference?यदि AP का पहला पद (22) और (a_{32}=177) है तो सार्व अंतर क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 55
For an AP, \(a_n=a+(n-1)d\). Here, \(a=22\), \(n=32\), and \(a_{32}=177\). Thus, \(177=22+31d\), so \(31d=155\) and \(d=5\). If the common difference were 4, the 32nd term would be \(22+31\times4=146\), not 177. Exam tip: the common difference is added \(n-1\) times to obtain the \(n\)th term.AP के लिए सूत्र है: \(a_n=a+(n-1)d\)। यहाँ \(a=22\), \(n=32\) और \(a_{32}=177\) है। अतः \(177=22+31d\), इसलिए \(31d=155\) और \(d=5\)। विकल्प 4 लेने पर 32वाँ पद \(22+31\times4=146\) होगा, जो 177 नहीं है। परीक्षा टिप: \(n\)वें पद में \(n-1\) बार सार्व अंतर जुड़ता है।
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