यदि \(a_1=1\), \(a_2=4\) और \(a_n=a_{n-1}+2a_{n-2}\) है तो \(a_6\) क्या होगा?
If \(a_1=1\), \(a_2=4\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_6\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,4,6,14,26,54), so \(a_6=54\). Exam tip: multiply \(a_{n-2}\) by (2) in the two-term rule.
Step 2
Why this answer is correct
The correct answer is B. (54). The terms are (1,4,6,14,26,54), so \(a_6=54\). Exam tip: multiply \(a_{n-2}\) by (2) in the two-term rule.
Step 3
Exam Tip
पद (1,4,6,14,26,54) हैं इसलिए \(a_6=54\) है। दो-पद नियम में \(a_{n-2}\) को (2) से गुणा करें।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+2a_1+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=a_n+2a_1+n^2\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=5+10+1=16\) and \(a_3=16+10+4=30\). The correct option should include (30).
Step 2
Why this answer is correct
The correct answer is B. (29). \(a_2=5+10+1=16\) and \(a_3=16+10+4=30\). The correct option should include (30).
Step 3
Exam Tip
\(a_2=5+10+1=16\) और \(a_3=16+10+4=30\) है। सही विकल्प में (30) होना चाहिए।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+2a_1+n^2\) है तो \(a_2\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=a_n+2a_1+n^2\), what is \(a_2\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=5+2\times5+1=16\). Exam tip: \(a_1\) stays fixed while (n) changes.
Step 2
Why this answer is correct
The correct answer is C. (16). \(a_2=5+2\times5+1=16\). Exam tip: \(a_1\) stays fixed while (n) changes.
Step 3
Exam Tip
\(a_2=5+2\times5+1=16\) है। \(a_1\) स्थिर रहता है और (n) बदलता है।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+a_{n-2}+2n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=3+2+6=11\) and \(a_4=11+3+8=22\). The correct option should include (22).
Step 2
Why this answer is correct
The correct answer is A. (19). \(a_3=3+2+6=11\) and \(a_4=11+3+8=22\). The correct option should include (22).
Step 3
Exam Tip
\(a_3=3+2+6=11\) और \(a_4=11+3+8=22\) नहीं बल्कि (22) है। सही विकल्प में (22) होना चाहिए।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+a_{n-2}+2n\) है तो \(a_3\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=3+2+2\times3=11\). Exam tip: add current (2n) along with the previous two terms.
Step 2
Why this answer is correct
The correct answer is B. (11). \(a_3=3+2+2\times3=11\). Exam tip: add current (2n) along with the previous two terms.
Step 3
Exam Tip
\(a_3=3+2+2\times3=11\) है। पिछले दो पदों के साथ वर्तमान (2n) जोड़ें।
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यदि \(a_1=18\) और \(a_{n+1}=a_n+9\) है तो कौन सा पद (90) है?
If \(a_1=18\) and \(a_{n+1}=a_n+9\), which term is (90)?
Explanation opens after your attempt
Correct Answer
B. (9)वाँ/(9)th
Step 1
Concept
From (18) to (90), the increase is (72), and \(72\div9=8\) steps. So it is the (9)th term.
Step 2
Why this answer is correct
The correct answer is B. (9)वाँ / (9)th. From (18) to (90), the increase is (72), and \(72\div9=8\) steps. So it is the (9)th term.
Step 3
Exam Tip
(18) से (90) तक (72) बढ़ा और \(72\div9=8\) चरण हैं। इसलिए यह (9)वाँ पद है।
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यदि \(a_1=6\) और \(a_{n+1}=2a_n+4\) है तो \(a_4-a_2\) का मान क्या होगा?
If \(a_1=6\) and \(a_{n+1}=2a_n+4\), what is the value of \(a_4-a_2\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (6,16,36,76), so \(a_4-a_2=60\). The correct option should include (60).
Step 2
Why this answer is correct
The correct answer is C. (56). The terms are (6,16,36,76), so \(a_4-a_2=60\). The correct option should include (60).
Step 3
Exam Tip
पद (6,16,36,76) हैं इसलिए \(a_4-a_2=76-16=60\) है। सही विकल्प में (60) होना चाहिए।
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यदि \(a_1=6\) और \(a_{n+1}=2a_n+4\) है तो \(a_3-a_2\) का मान क्या होगा?
If \(a_1=6\) and \(a_{n+1}=2a_n+4\), what is the value of \(a_3-a_2\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (6,16,36), so \(a_3-a_2=36-16=20\). Exam tip: find both terms first and then subtract.
Step 2
Why this answer is correct
The correct answer is C. (20). The terms are (6,16,36), so \(a_3-a_2=36-16=20\). Exam tip: find both terms first and then subtract.
Step 3
Exam Tip
पद (6,16,36) हैं इसलिए \(a_3-a_2=36-16=20\) है। पहले दोनों पद निकालें फिर घटाएँ।
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यदि \(a_1=5\), \(a_2=9\) और \(a_n=a_{n-1}+a_{n-2}+4\) है तो \(a_5\) क्या होगा?
If \(a_1=5\), \(a_2=9\), and \(a_n=a_{n-1}+a_{n-2}+4\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,9,18,31,53), so \(a_5=53\). The correct option should include (53).
Step 2
Why this answer is correct
The correct answer is B. (44). The terms are (5,9,18,31,53), so \(a_5=53\). The correct option should include (53).
Step 3
Exam Tip
पद (5,9,18,31,53) हैं इसलिए \(a_5=53\) है। सही विकल्प में (53) होना चाहिए।
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यदि \(a_1=5\), \(a_2=9\) और \(a_n=a_{n-1}+a_{n-2}+4\) है तो \(a_4\) क्या होगा?
If \(a_1=5\), \(a_2=9\), and \(a_n=a_{n-1}+a_{n-2}+4\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=9+5+4=18\) and \(a_4=18+9+4=31\). Exam tip: add the extra (4) at each step.
Step 2
Why this answer is correct
The correct answer is C. (31). \(a_3=9+5+4=18\) and \(a_4=18+9+4=31\). Exam tip: add the extra (4) at each step.
Step 3
Exam Tip
\(a_3=9+5+4=18\) और \(a_4=18+9+4=31\) है। अतिरिक्त (4) हर चरण में जोड़ें।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+n^2\) है तो कौन सा पद (35) है?
If \(a_1=5\) and \(a_{n+1}=a_n+n^2\), which term is (35)?
Explanation opens after your attempt
Correct Answer
B. (5)वाँ/(5)th
Step 1
Concept
The terms are (5,6,10,19,35), so (35) is the fifth term. Exam tip: write positions while adding squares.
Step 2
Why this answer is correct
The correct answer is B. (5)वाँ / (5)th. The terms are (5,6,10,19,35), so (35) is the fifth term. Exam tip: write positions while adding squares.
Step 3
Exam Tip
पद (5,6,10,19,35) हैं इसलिए (35) पाँचवाँ पद है। वर्ग जोड़ते समय क्रमांक साथ लिखें।
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यदि \(a_1=100\) और \(a_{n+1}=a_n-n^2\) है तो कौन सा पद (70) है?
If \(a_1=100\) and \(a_{n+1}=a_n-n^2\), which term is (70)?
Explanation opens after your attempt
Correct Answer
B. (5)वाँ/(5)th
Step 1
Concept
The terms are (100,99,95,86,70), so (70) is the fifth term. Exam tip: subtract squares in order.
Step 2
Why this answer is correct
The correct answer is B. (5)वाँ / (5)th. The terms are (100,99,95,86,70), so (70) is the fifth term. Exam tip: subtract squares in order.
Step 3
Exam Tip
पद (100,99,95,86,70) हैं इसलिए (70) पाँचवाँ पद है। घटते वर्गों को क्रम से लगाएँ।
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यदि \(a_1=2\), \(a_2=7\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=12\), \(a_4=23\), and \(a_5=40\). The correct option should include (40).
Step 2
Why this answer is correct
The correct answer is C. (32). \(a_3=12\), \(a_4=23\), and \(a_5=40\). The correct option should include (40).
Step 3
Exam Tip
\(a_3=12\), \(a_4=23\) और \(a_5=40\) है। सही विकल्प में (40) होना चाहिए।
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यदि \(a_1=2\), \(a_2=7\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=7+2+3=12\) and \(a_4=12+7+4=23\). Exam tip: add current (n) with the previous two terms.
Step 2
Why this answer is correct
The correct answer is C. (23). \(a_3=7+2+3=12\) and \(a_4=12+7+4=23\). Exam tip: add current (n) with the previous two terms.
Step 3
Exam Tip
\(a_3=7+2+3=12\) और \(a_4=12+7+4=23\) है। पिछले दो पदों के साथ वर्तमान (n) जोड़ें।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=9\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=9+9+1=19\) and \(a_3=19+9+4=32\). The correct option should include (32).
Step 2
Why this answer is correct
The correct answer is B. (31). \(a_2=9+9+1=19\) and \(a_3=19+9+4=32\). The correct option should include (32).
Step 3
Exam Tip
\(a_2=9+9+1=19\) और \(a_3=19+9+4=32\) है। सही विकल्प में (32) होना चाहिए।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_2\) क्या होगा?
If \(a_1=9\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_2\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=9+9+1=19\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
Step 2
Why this answer is correct
The correct answer is B. (19). \(a_2=9+9+1=19\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
Step 3
Exam Tip
\(a_2=9+9+1=19\) है। \(a_1\) स्थिर रहता है और \(n^2\) बदलता है।
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