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If the (19)th term of the AP (z,z+5,z+10,\ldots) is (112), what is (z)?यदि AP (z,z+5,z+10,\ldots) का (19)वां पद (112) है तो (z) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 2222
Here, the first term is \(a=z\) and the common difference is \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(112=z+(19-1)\times5=z+90\), so \(z=22\). If 20 were used, the 19th term would be \(20+90=110\), not 112. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.इस AP का प्रथम पद \(a=z\) और सार्वांतर \(d=5\) है। \(n\)वाँ पद \(a_n=a+(n-1)d\) होता है। अतः \(112=z+(19-1)\times5=z+90\), इसलिए \(z=22\)। विकल्प 20 लेने पर 19वाँ पद \(20+90=110\) आएगा, जो सही नहीं है। परीक्षा टिप: \(n\)वें पद के सूत्र में \(n-1\) का प्रयोग करना न भूलें।
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