0 reads0 ratings0 helpful
If (a=6) and (a_7=384), and (r) is positive, what is (r)?यदि (a=6) और (a_7=384) है तथा (r) धनात्मक है, तो (r) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(2\)\(2\)
In a geometric progression, the seventh term is \(a_7=ar^6\). Thus, \(384=6r^6\), so \(r^6=64=2^6\). Since \(r\) is stated to be positive, \(r=2\). Although \(r=-2\) also satisfies \(r^6=64\), it violates the given condition. Exam tip: in \(a_n=ar^{n-1}\), the exponent of \(r\) is always \(n-1\).गुणोत्तर श्रेणी में सातवाँ पद \(a_7=ar^6\) होता है। अतः \(384=6r^6\), इसलिए \(r^6=64=2^6\)। चूँकि \(r\) धनात्मक दिया है, इसलिए \(r=2\) होगा। \(r=-2\) भी \(r^6=64\) को संतुष्ट करता, पर वह दी गई शर्त के विरुद्ध है। परीक्षा टिप: \(n\)वें पद के सूत्र \(a_n=ar^{n-1}\) में घात \(n-1\) होती है।
Student feedback
Was this question useful?
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Difficulty
Easy0%
Medium0%
Hard0%
Was the explanation clear?
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
