अनुक्रम \(3,9,27,81,\ldots\) में recursive rule का गुणक क्या है?
In the sequence \(3,9,27,81,\ldots\), what is the multiplier in the recursive rule?
Correct answer and explanation
B. 3
Simple Explanation
इस अनुक्रम में प्रत्येक पद पिछले पद को 3 से गुणा करके मिलता है: \(3\times3=9\), \(9\times3=27\) और \(27\times3=81\)। अतः recursive rule \(a_n=3a_{n-1}\) है, इसलिए गुणक 3 है। 9 एक पद है, गुणक नहीं। परीक्षा टिप: लगातार दो पदों का भाग लेकर गुणक जाँचें, जैसे \(27\div9=3\)। / Each term is obtained by multiplying the previous term by 3: \(3\times3=9\), \(9\times3=27\), and \(27\times3=81\). Thus, the recursive rule is \(a_n=3a_{n-1}\), so the multiplier is 3. Although 9 is a term of the sequence, it is not the multiplier. Exam tip: divide a term by the preceding term, for example \(27\div9=3\), to find the multiplier.
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