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If the (12)th term of the AP (y,y+6,y+12,\ldots) is (89), what is the value of (y)?यदि समान्तर श्रेणी (y,y+6,y+12,\ldots) का (12)वां पद (89) है तो (y) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(23\)\(23\)
For this AP, the first term is \(a=y\) and the common difference is \(d=6\). The 12th term is \(a_{12}=a+(12-1)d\). Therefore, \(89=y+11\times6=y+66\), so \(y=23\). If \(y=21\), the 12th term would be \(87\), not \(89\). Exam tip: use \(n-1\), not \(n\), in the nth-term formula.इस समान्तर श्रेणी में प्रथम पद \(a=y\) और सार्वांतर \(d=6\) है। \(12\)वां पद \(a_{12}=a+(12-1)d\) होगा। अतः \(89=y+11\times6=y+66\), इसलिए \(y=23\)। \(21\) लेने पर \(12\)वां पद \(87\) आता है, इसलिए वह सही नहीं है। परीक्षा टिप: \(n\)वें पद के सूत्र में \(n-1\) का प्रयोग करें।
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