Question 1 / 10
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Time 05:00
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}+a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=2a_{n-1}+a_{n-2}\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,12,29,70), so \(a_5=70\). Exam tip: use both previous terms in a two-term rule.
Step 2
Why this answer is correct
The correct answer is C. (70). The terms are (2,5,12,29,70), so \(a_5=70\). Exam tip: use both previous terms in a two-term rule.
Step 3
Exam Tip
पद (2,5,12,29,70) हैं इसलिए \(a_5=70\) है। दो-पद नियम में दोनों पिछले पदों का उपयोग करें।
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यदि \(a_1=1\), \(a_2=4\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_5\) क्या होगा?
If \(a_1=1\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,4,8,16,29), so \(a_5=29\). Exam tip: add the current (n) with the previous two terms.
Step 2
Why this answer is correct
The correct answer is C. (29). The terms are (1,4,8,16,29), so \(a_5=29\). Exam tip: add the current (n) with the previous two terms.
Step 3
Exam Tip
पद (1,4,8,16,29) हैं इसलिए \(a_5=29\) है। पिछले दो पदों के साथ वर्तमान (n) जोड़ें।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+4\) है तो कौन सा पद (53) है?
If \(a_1=9\) and \(a_{n+1}=a_n+4\), which term is (53)?
Explanation opens after your attempt
Correct Answer
C. (12)वाँ/(12)th
Step 1
Concept
(53-9=44), and \(44\div4=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.
Step 2
Why this answer is correct
The correct answer is C. (12)वाँ / (12)th. (53-9=44), and \(44\div4=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.
Step 3
Exam Tip
(53-9=44) और \(44\div4=11\) चरण हैं इसलिए पद संख्या (12) है। चरणों में (1) जोड़कर पद संख्या मिलती है।
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यदि \(a_1=3\) और \(a_{n+1}=2a_n+5\) है तो \(a_4-a_2\) का मान क्या होगा?
If \(a_1=3\) and \(a_{n+1}=2a_n+5\), what is the value of \(a_4-a_2\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,11,27,59), so \(a_4-a_2=48\). Exam tip: find both terms first and subtract.
Step 2
Why this answer is correct
The correct answer is C. (48). The terms are (3,11,27,59), so \(a_4-a_2=48\). Exam tip: find both terms first and subtract.
Step 3
Exam Tip
पद (3,11,27,59) हैं इसलिए \(a_4-a_2=48\) है। पहले दोनों पद निकालकर घटाएँ।
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यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+5\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+5\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,6,13,24,42), so \(a_5=42\). Exam tip: add (5) along with the previous two terms.
Step 2
Why this answer is correct
The correct answer is C. (42). The terms are (2,6,13,24,42), so \(a_5=42\). Exam tip: add (5) along with the previous two terms.
Step 3
Exam Tip
पद (2,6,13,24,42) हैं इसलिए \(a_5=42\) है। पिछले दो पदों के साथ (5) भी जोड़ें।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=2a_{n-1}+3a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=2a_{n-1}+3a_{n-2}\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times3+3\times2=12\) and \(a_4=2\times12+3\times3=33\). Exam tip: apply coefficients to the correct terms.
Step 2
Why this answer is correct
The correct answer is C. (33). \(a_3=2\times3+3\times2=12\) and \(a_4=2\times12+3\times3=33\). Exam tip: apply coefficients to the correct terms.
Step 3
Exam Tip
\(a_3=2\times3+3\times2=12\) और \(a_4=2\times12+3\times3=33\) है। गुणांकों को सही पदों पर लगाएँ।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+2a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=3+2\times2+3=10\) and \(a_4=10+2\times3+4=20\). Exam tip: do not forget to add the current (n).
Step 2
Why this answer is correct
The correct answer is C. (20). \(a_3=3+2\times2+3=10\) and \(a_4=10+2\times3+4=20\). Exam tip: do not forget to add the current (n).
Step 3
Exam Tip
\(a_3=3+2\times2+3=10\) और \(a_4=10+2\times3+4=20\) है। वर्तमान (n) भी जोड़ना न भूलें।
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यदि \(a_1=8\) और \(a_{n+1}=\frac{a_n}{2}+a_1\) है तो \(a_4\) क्या होगा?
If \(a_1=8\) and \(a_{n+1}=\frac{a_n}{2}+a_1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (8,12,14,15), so \(a_4=15\). Exam tip: \(a_1\) stays fixed and half of the previous term is used.
Step 2
Why this answer is correct
The correct answer is C. (15). The terms are (8,12,14,15), so \(a_4=15\). Exam tip: \(a_1\) stays fixed and half of the previous term is used.
Step 3
Exam Tip
पद (8,12,14,15) हैं इसलिए \(a_4=15\) है। \(a_1\) स्थिर रहता है और पिछले पद का आधा लिया जाता है।
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यदि \(a_1=7\) और \(a_{n+1}=a_n+na_1\) है तो \(a_4\) क्या होगा?
If \(a_1=7\) and \(a_{n+1}=a_n+na_1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (7,14,28,49), so \(a_4=49\). Exam tip: \(a_1\) is fixed while (n) changes.
Step 2
Why this answer is correct
The correct answer is C. (49). The terms are (7,14,28,49), so \(a_4=49\). Exam tip: \(a_1\) is fixed while (n) changes.
Step 3
Exam Tip
पद (7,14,28,49) हैं इसलिए \(a_4=49\) है। \(a_1\) स्थिर है और (n) बदलता है।
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}+a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=2a_{n-1}+a_{n-2}+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times5+2+3=15\) and \(a_4=2\times15+5+4=39\). Exam tip: add the current (n) also in a two-term rule.
Step 2
Why this answer is correct
The correct answer is C. (39). \(a_3=2\times5+2+3=15\) and \(a_4=2\times15+5+4=39\). Exam tip: add the current (n) also in a two-term rule.
Step 3
Exam Tip
\(a_3=2\times5+2+3=15\) और \(a_4=2\times15+5+4=39\) है। दो-पद नियम में वर्तमान (n) भी जोड़ें।
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