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अनुक्रम \(81,27,9,3,\ldots\) में प्रत्येक पद पिछले पद का \(\frac{1}{3}\) है। छठा पद क्या होगा?
In the sequence \(81,27,9,3,\ldots\), each term is \(\frac{1}{3}\) of the previous term. What is the sixth term?
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3}\)
Step 1
Concept
The terms are \(81,27,9,3,1,\frac{1}{3}\). Exam tip: divide each term by (3) step by step.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). The terms are \(81,27,9,3,1,\frac{1}{3}\). Exam tip: divide each term by (3) step by step.
Step 3
Exam Tip
पद हैं \(81,27,9,3,1,\frac{1}{3}\)। क्रम से घटाते समय हर पद को \(\frac{3}{1}\) से न बाँटें बल्कि (3) से बाँटें।
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अनुक्रम \(5,10,20,40,\ldots\) में कौन सा पद (320) है?
In the sequence \(5,10,20,40,\ldots\), which term is (320)?
Explanation opens after your attempt
Correct Answer
C. (7)वाँ/(7)th
Step 1
Concept
The terms are \(5\times2^{n-1}\), and \(5\times2^6=320\). Hence it is the (7)th term.
Step 2
Why this answer is correct
The correct answer is C. (7)वाँ / (7)th. The terms are \(5\times2^{n-1}\), and \(5\times2^6=320\). Hence it is the (7)th term.
Step 3
Exam Tip
पद \(5\times2^{n-1}\) हैं और \(5\times2^6=320\) है। इसलिए यह (7)वाँ पद है।
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अनुक्रम \(2,6,18,54,\ldots\) में \(a_1=2\) और \(a_{n+1}=3a_n\) है। \(a_6\) क्या है?
In the sequence \(2,6,18,54,\ldots\), \(a_1=2\) and \(a_{n+1}=3a_n\). What is \(a_6\)?
Explanation opens after your attempt
Step 1
Concept
\(a_6=2\times3^5=486\). Exam tip: when starting from the first term, the exponent is (n-1).
Step 2
Why this answer is correct
The correct answer is D. (486). \(a_6=2\times3^5=486\). Exam tip: when starting from the first term, the exponent is (n-1).
Step 3
Exam Tip
\(a_6=2\times3^5=486\) है। पहले पद से गिनते समय घात (n-1) होती है।
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अनुक्रम \(1,-2,4,-8,16,\ldots\) में आठवाँ पद क्या होगा?
What will be the eighth term in the sequence \(1,-2,4,-8,16,\ldots\)?
Explanation opens after your attempt
Step 1
Concept
Each term is multiplied by (-2), so the eighth term is ((-2)7=-128). Exam tip: track both sign and power.
Step 2
Why this answer is correct
The correct answer is D. (-128). Each term is multiplied by (-2), so the eighth term is ((-2)7=-128). Exam tip: track both sign and power.
Step 3
Exam Tip
हर बार (-2) से गुणा हो रहा है इसलिए आठवाँ पद ((-2)7=-128) है। संकेत और घात दोनों साथ देखें।
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अनुक्रम \(5,-10,20,-40,\ldots\) में सातवाँ पद क्या है?
What is the seventh term in the sequence \(5,-10,20,-40,\ldots\)?
Explanation opens after your attempt
Step 1
Concept
The general term is (a_n=5(-2)^{n-1}), so (a_7=5(-2)6=320). Exam tip: an even power gives a positive sign.
Step 2
Why this answer is correct
The correct answer is C. (320). The general term is (a_n=5(-2)^{n-1}), so (a_7=5(-2)6=320). Exam tip: an even power gives a positive sign.
Step 3
Exam Tip
सामान्य पद (a_n=5(-2)^{n-1}) है इसलिए (a_7=5(-2)6=320) है। सम घात पर चिह्न धनात्मक होता है।
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