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Which of the following formulae does not represent the \(n\)th term of an arithmetic progression (AP) for every positive integer \(n\)?निम्नलिखित में से कौन-सा सूत्र प्रत्येक धनात्मक पूर्णांक \(n\) के लिए समानांतर श्रेणी (AP) का \(n\)वाँ पद निरूपित नहीं करता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a_n=n^2+1\)\(a_n=n^2+1\)
The general term of an AP is \(a_n=a+(n-1)d\), which is linear in \(n\). Since \(n^2+1\) contains a squared term, its consecutive differences are not constant. Exam tip: a quadratic term usually indicates that the sequence is not an AP.AP के \(n\)वें पद का सामान्य रूप \(a_n=a+(n-1)d\) होता है, जो \(n\) का रैखिक व्यंजक है। \(n^2+1\) में वर्ग पद है, इसलिए क्रमागत पदों के अंतर समान नहीं होंगे। परीक्षा में \(n^2\) वाला पद दिखे तो उसे AP न मानें।
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