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अनुक्रम \(3,6,12,24,\ldots\) में पहला पद जो (500) से बड़ा है कौन सा है?
In the sequence \(3,6,12,24,\ldots\), which is the first term greater than (500)?
#sequences
#geometric
#first-term
#class-9
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
Explanation opens after your attempt
Correct Answer
B. (9)वाँ / (9)th
Step 1
Concept
\(a_8=384\) and \(a_9=768\), so the first greater term is the (9)th. Exam tip: check terms on both sides of the boundary.
Step 2
Why this answer is correct
The correct answer is B. (9)वाँ / (9)th. \(a_8=384\) and \(a_9=768\), so the first greater term is the (9)th. Exam tip: check terms on both sides of the boundary.
Step 3
Exam Tip
\(a_8=384\) और \(a_9=768\) है इसलिए पहला बड़ा पद (9)वाँ है। सीमा के दोनों ओर के पद जाँचें।
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अनुक्रम \(8,16,32,64,\ldots\) के पहले (5) पदों का औसत क्या है?
What is the average of the first (5) terms of the sequence \(8,16,32,64,\ldots\)?
#sequences
#average
#geometric
#class-9
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A (48)
B (49.6)
C (50.4)
D (51.2)
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Step 1
Concept
The sum of the first (5) terms is (8+16+32+64+128=248). The average is \(\frac{248}{5}=49.6\).
Step 2
Why this answer is correct
The correct answer is B. (49.6). The sum of the first (5) terms is (8+16+32+64+128=248). The average is \(\frac{248}{5}=49.6\).
Step 3
Exam Tip
पहले (5) पदों का योग (8+16+32+64+128=248) है। औसत \(\frac{248}{5}=49.6\) होगा।
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अनुक्रम \(5,10,20,40,\ldots\) में कौन सा पद (5120) है?
In the sequence \(5,10,20,40,\ldots\), which term is (5120)?
#sequences
#geometric
#term-position
#class-9
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A (10)वाँ / (10)th
B (11)वाँ / (11)th
C (12)वाँ / (12)th
D (13)वाँ / (13)th
Explanation opens after your attempt
Correct Answer
B. (11)वाँ / (11)th
Step 1
Concept
\(5\times2^{10}=5120\), so it is the (11)th term. Exam tip: from the first term, the exponent is (n-1).
Step 2
Why this answer is correct
The correct answer is B. (11)वाँ / (11)th. \(5\times2^{10}=5120\), so it is the (11)th term. Exam tip: from the first term, the exponent is (n-1).
Step 3
Exam Tip
\(5\times2^{10}=5120\) है इसलिए यह (11)वाँ पद है। पहले पद से गिनते समय घात (n-1) होती है।
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