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What is the (5)th term of the geometric progression (3,12,48,\ldots)?गुणोत्तर श्रेढ़ी (3,12,48,\ldots) का (5)वाँ पद क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 768768
The first term is \(a=3\) and the common ratio is \(r=\frac{12}{3}=4\). The nth term of a GP is \(a_n=ar^{n-1}\). Therefore, \(a_5=3\times4^{5-1}=3\times4^4=768\). Option 384 is a close distractor, but it equals \(3\times4^3\), which is the fourth term. Exam tip: in the nth-term formula, the exponent is always \(n-1\).इस गुणोत्तर श्रेढ़ी का प्रथम पद \(a=3\) और सार्व अनुपात \(r=\frac{12}{3}=4\) है। \(n\)वाँ पद \(a_n=ar^{n-1}\) होता है। अतः \(a_5=3\times4^{5-1}=3\times4^4=768\)। 384 निकट का विकल्प है, लेकिन वह \(3\times4^3\) है, अर्थात चौथा पद। परीक्षा टिप: \(n\)वें पद में घात हमेशा \(n-1\) होती है।
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