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If the first term of an AP is (9) and (a_{21}=69), what is (d)?यदि समान्तर श्रेणी का पहला पद (9) और (a_{21}=69) है, तो (d) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 33
The nth-term formula of an AP is \(a_n=a+(n-1)d\). Here, \(a=9\) and \(a_{21}=69\), so \(69=9+(21-1)d=9+20d\). Hence, \(20d=60\), giving \(d=3\). If 2 were used, the 21st term would be \(9+20\times2=49\), not 69. Exam tip: the nth term contains \((n-1)d\), not \(nd\).समान्तर श्रेणी के nवें पद का सूत्र \(a_n=a+(n-1)d\) है। यहाँ \(a=9\), \(a_{21}=69\) है, इसलिए \(69=9+(21-1)d=9+20d\)। अतः \(20d=60\), इसलिए \(d=3\)। विकल्प 2 लेने पर 21वाँ पद \(9+20\times2=49\) होगा, 69 नहीं। परीक्षा टिप: \(n\)वें पद में हमेशा \((n-1)d\) होता है, \(nd\) नहीं।
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