यदि \(a_1=3\) और \(a_{n+1}=a_n+2n+1\) है तो \(a_5\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n+2n+1\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,6,11,18,27), so \(a_5=27\). Exam tip: use the changing value of (n) correctly at each step.
Step 2
Why this answer is correct
The correct answer is C. (27). The terms are (3,6,11,18,27), so \(a_5=27\). Exam tip: use the changing value of (n) correctly at each step.
Step 3
Exam Tip
पद (3,6,11,18,27) मिलते हैं इसलिए \(a_5=27\) है। बदलते (n) का मान हर चरण में सही रखें।
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यदि \(a_1=40\) और \(a_{n+1}=a_n-3n\) है तो \(a_4\) क्या होगा?
If \(a_1=40\) and \(a_{n+1}=a_n-3n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (40,37,31,22), so \(a_4=22\). Exam tip: calculate (3n) separately before subtracting.
Step 2
Why this answer is correct
The correct answer is D. (22). The terms are (40,37,31,22), so \(a_4=22\). Exam tip: calculate (3n) separately before subtracting.
Step 3
Exam Tip
पद (40,37,31,22) हैं इसलिए \(a_4=22\) है। घटाव में (3n) का मान अलग-अलग निकालें।
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यदि \(a_1=2\) और \(a_{n+1}=2a_n+n\) है तो \(a_4\) का मान क्या होगा?
If \(a_1=2\) and \(a_{n+1}=2a_n+n\), what is the value of \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,12,27), so \(a_4=27\). Exam tip: double the previous term first and then add (n).
Step 2
Why this answer is correct
The correct answer is C. (27). The terms are (2,5,12,27), so \(a_4=27\). Exam tip: double the previous term first and then add (n).
Step 3
Exam Tip
पद (2,5,12,27) हैं इसलिए \(a_4=27\) है। पहले पिछले पद को दोगुना करें फिर (n) जोड़ें।
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यदि \(a_1=5\) और \(a_{n+1}=2a_n-2n\) है तो \(a_4\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=2a_n-2n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,8,12,18), so \(a_4=18\). The correct option should include (18).
Step 2
Why this answer is correct
The correct answer is D. (26). The terms are (5,8,12,18), so \(a_4=18\). The correct option should include (18).
Step 3
Exam Tip
पद (5,8,12,18) नहीं बल्कि \(a_4=18\) होता है। इस प्रश्न के लिए सही विकल्पों में (18) होना चाहिए।
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यदि \(a_1=5\) और \(a_{n+1}=2a_n-2n\) है तो \(a_3\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=2a_n-2n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,8,12), so \(a_3=12\). Exam tip: do not change the order of multiplication and subtraction.
Step 2
Why this answer is correct
The correct answer is C. (12). The terms are (5,8,12), so \(a_3=12\). Exam tip: do not change the order of multiplication and subtraction.
Step 3
Exam Tip
पद (5,8,12) हैं इसलिए \(a_3=12\) है। गुणा और घटाव का क्रम न बदलें।
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यदि \(a_1=1\), \(a_2=4\) और \(a_n=a_{n-1}+2a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=1\), \(a_2=4\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,4,6,14,26), so \(a_5=26\). Exam tip: multiply the second previous term by (2).
Step 2
Why this answer is correct
The correct answer is C. (26). The terms are (1,4,6,14,26), so \(a_5=26\). Exam tip: multiply the second previous term by (2).
Step 3
Exam Tip
पद (1,4,6,14,26) हैं इसलिए \(a_5=26\) है। पिछले दो पदों में दूसरे पिछले पद को (2) से गुणा करें।
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}-a_{n-2}\) है तो \(a_6\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=2a_{n-1}-a_{n-2}\), what is \(a_6\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,8,11,14,17), so \(a_6=17\). Exam tip: write positions while using two-term rules.
Step 2
Why this answer is correct
The correct answer is C. (17). The terms are (2,5,8,11,14,17), so \(a_6=17\). Exam tip: write positions while using two-term rules.
Step 3
Exam Tip
पद (2,5,8,11,14,17) हैं इसलिए \(a_6=17\) है। दो-पद नियम में क्रमांक साथ लिखें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n+n^2\) है तो \(a_5\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n+n^2\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,4,8,17,33), so \(a_5=33\). Exam tip: add \(1^2,2^2,3^2,4^2\) in order.
Step 2
Why this answer is correct
The correct answer is B. (30). The terms are (3,4,8,17,33), so \(a_5=33\). Exam tip: add \(1^2,2^2,3^2,4^2\) in order.
Step 3
Exam Tip
पद (3,4,8,17,33) नहीं बल्कि \(a_5=33\) है। वर्ग जोड़ते समय \(1^2,2^2,3^2,4^2\) जोड़ें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n+n^2\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,4,8,17), so \(a_4=17\). Exam tip: add the new value of \(n^2\) at each step.
Step 2
Why this answer is correct
The correct answer is C. (17). The terms are (3,4,8,17), so \(a_4=17\). Exam tip: add the new value of \(n^2\) at each step.
Step 3
Exam Tip
पद (3,4,8,17) हैं इसलिए \(a_4=17\) है। हर चरण में \(n^2\) का नया मान जोड़ें।
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यदि \(a_1=50\) और (a_{n+1}=a_n-(2n+3)) है तो \(a_4\) क्या होगा?
If \(a_1=50\) and (a_{n+1}=a_n-(2n+3)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (50,45,38,29), so \(a_4=29\). Exam tip: calculate (2n+3) before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (29). The terms are (50,45,38,29), so \(a_4=29\). Exam tip: calculate (2n+3) before subtracting.
Step 3
Exam Tip
पद (50,45,38,29) हैं इसलिए \(a_4=29\) है। (2n+3) को घटाने से पहले सही मान निकालें।
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यदि \(a_1=2\) और \(a_{n+1}=3a_n+1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=3a_n+1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,7,22,67), so \(a_4=67\). The option (67) is correct.
Step 2
Why this answer is correct
The correct answer is C. (64). The terms are (2,7,22,67), so \(a_4=67\). The option (67) is correct.
Step 3
Exam Tip
पद (2,7,22,67) नहीं बल्कि \(a_4=67\) है। अंतिम विकल्प (67) सही होना चाहिए।
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यदि \(a_1=2\) और \(a_{n+1}=3a_n+1\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=3a_n+1\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,7,22), so \(a_3=22\). Exam tip: multiply by (3) first and then add (1).
Step 2
Why this answer is correct
The correct answer is C. (22). The terms are (2,7,22), so \(a_3=22\). Exam tip: multiply by (3) first and then add (1).
Step 3
Exam Tip
पद (2,7,22) हैं इसलिए \(a_3=22\) है। पहले (3) से गुणा करें फिर (1) जोड़ें।
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यदि \(a_1=10\) और \(a_{n+1}=\frac{a_n}{2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=10\) and \(a_{n+1}=\frac{a_n}{2}+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (10,6,5,5.5), so \(a_4=5.5\). Exam tip: halve first and then add (n).
Step 2
Why this answer is correct
The correct answer is D. (8.5). The terms are (10,6,5,5.5), so \(a_4=5.5\). Exam tip: halve first and then add (n).
Step 3
Exam Tip
पद (10,6,5,5.5) नहीं बल्कि \(a_4=5.5\) है। आधा करने के बाद (n) जोड़ें।
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यदि \(a_1=10\) और \(a_{n+1}=\frac{a_n}{2}+n\) है तो \(a_3\) क्या होगा?
If \(a_1=10\) and \(a_{n+1}=\frac{a_n}{2}+n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (10,6,5), so \(a_3=5\). Exam tip: halve the previous term first and then add (n).
Step 2
Why this answer is correct
The correct answer is B. (5). The terms are (10,6,5), so \(a_3=5\). Exam tip: halve the previous term first and then add (n).
Step 3
Exam Tip
पद (10,6,5) हैं इसलिए \(a_3=5\) है। पहले पिछले पद का आधा करें फिर (n) जोड़ें।
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यदि \(a_1=1\), \(a_2=3\) और \(a_n=2a_{n-1}+a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=1\), \(a_2=3\), and \(a_n=2a_{n-1}+a_{n-2}\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,7,17,41), so \(a_5=41\). The listed options do not include \(a_5\).
Step 2
Why this answer is correct
The correct answer is B. (17). The terms are (1,3,7,17,41), so \(a_5=41\). The listed options do not include \(a_5\).
Step 3
Exam Tip
पद (1,3,7,17,41) नहीं बल्कि \(a_4=17\) और \(a_5=41\) है। दिए गए विकल्पों में \(a_5\) नहीं है।
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यदि \(a_1=1\), \(a_2=3\) और \(a_n=2a_{n-1}+a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=1\), \(a_2=3\), and \(a_n=2a_{n-1}+a_{n-2}\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,7,17), so \(a_4=17\). Exam tip: multiply \(a_{n-1}\) by (2) in this two-term rule.
Step 2
Why this answer is correct
The correct answer is C. (17). The terms are (1,3,7,17), so \(a_4=17\). Exam tip: multiply \(a_{n-1}\) by (2) in this two-term rule.
Step 3
Exam Tip
पद (1,3,7,17) हैं इसलिए \(a_4=17\) है। दो-पद नियम में \(a_{n-1}\) को (2) से गुणा करें।
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यदि \(a_1=4\) और \(a_{n+1}=a_n+3n-1\) है तो \(a_5\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+3n-1\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,6,11,19,30), so \(a_5=30\). The additions are (2,5,8,11).
Step 2
Why this answer is correct
The correct answer is C. (32). The terms are (4,6,11,19,30), so \(a_5=30\). The additions are (2,5,8,11).
Step 3
Exam Tip
पद (4,6,11,19,30) नहीं बल्कि \(a_5=30\) है। सही गणना में (2,5,8,11) जोड़े जाते हैं।
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यदि \(a_1=4\) और \(a_{n+1}=a_n+3n-1\) है तो \(a_4\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+3n-1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,6,11,19), so \(a_4=19\). Exam tip: (3n-1) has a new value at each step.
Step 2
Why this answer is correct
The correct answer is C. (19). The terms are (4,6,11,19), so \(a_4=19\). Exam tip: (3n-1) has a new value at each step.
Step 3
Exam Tip
पद (4,6,11,19) हैं इसलिए \(a_4=19\) है। (3n-1) का मान हर चरण में नया होता है।
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यदि \(a_1=2\) और \(a_{n+1}=a_n^2-1\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n^2-1\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=2^2-1=3\) and \(a_3=3^2-1=8\). Exam tip: square the previous term and subtract (1).
Step 2
Why this answer is correct
The correct answer is B. (8). \(a_2=2^2-1=3\) and \(a_3=3^2-1=8\). Exam tip: square the previous term and subtract (1).
Step 3
Exam Tip
\(a_2=2^2-1=3\) और \(a_3=3^2-1=8\) है। पिछले पद का वर्ग लेकर (1) घटाएँ।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+n+2\) है तो \(a_5\) का मान क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+n+2\), what is the value of \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (6,9,13,18,24), so \(a_5=24\). Exam tip: add the changing values of (n+2).
Step 2
Why this answer is correct
The correct answer is D. (24). The terms are (6,9,13,18,24), so \(a_5=24\). Exam tip: add the changing values of (n+2).
Step 3
Exam Tip
पद (6,9,13,18,24) हैं इसलिए \(a_5=24\) है। (n+2) के बदलते मान जोड़ें।
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यदि \(a_1=7\) और \(a_{n+1}=a_n+4n+1\) है तो \(a_4\) क्या होगा?
If \(a_1=7\) and \(a_{n+1}=a_n+4n+1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (7,12,21,34), so \(a_4=34\). Exam tip: calculate (4n+1) first and then add.
Step 2
Why this answer is correct
The correct answer is D. (34). The terms are (7,12,21,34), so \(a_4=34\). Exam tip: calculate (4n+1) first and then add.
Step 3
Exam Tip
पद (7,12,21,34) हैं इसलिए \(a_4=34\) है। पहले (4n+1) निकालें फिर जोड़ें।
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यदि \(a_1=80\) और \(a_{n+1}=\frac{a_n}{2}-n\) है तो \(a_3\) क्या होगा?
If \(a_1=80\) and \(a_{n+1}=\frac{a_n}{2}-n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=40-1=39\) and \(a_3=\frac{39}{2}-2=17.5\). So none of the options is correct.
Step 2
Why this answer is correct
The correct answer is A. (17). \(a_2=40-1=39\) and \(a_3=\frac{39}{2}-2=17.5\). So none of the options is correct.
Step 3
Exam Tip
\(a_2=40-1=39\) और \(a_3=\frac{39}{2}-2=17.5\) है। इसलिए दिए गए विकल्पों में सही मान नहीं है।
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यदि \(a_1=84\) और \(a_{n+1}=\frac{a_n}{2}-n\) है तो \(a_3\) क्या होगा?
If \(a_1=84\) and \(a_{n+1}=\frac{a_n}{2}-n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=42-1=41\) and \(a_3=\frac{41}{2}-2=18.5\). Check steps carefully before choosing integer options.
Step 2
Why this answer is correct
The correct answer is C. (19). \(a_2=42-1=41\) and \(a_3=\frac{41}{2}-2=18.5\). Check steps carefully before choosing integer options.
Step 3
Exam Tip
\(a_2=42-1=41\) और \(a_3=\frac{41}{2}-2=18.5\) नहीं है। सरल विकल्पों से बचने के लिए चरण जाँचें।
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यदि \(a_1=88\) और \(a_{n+1}=\frac{a_n}{2}-n\) है तो \(a_2\) क्या होगा?
If \(a_1=88\) and \(a_{n+1}=\frac{a_n}{2}-n\), what is \(a_2\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=\frac{88}{2}-1=43\). Exam tip: halve first and then subtract (n).
Step 2
Why this answer is correct
The correct answer is B. (43). \(a_2=\frac{88}{2}-1=43\). Exam tip: halve first and then subtract (n).
Step 3
Exam Tip
\(a_2=\frac{88}{2}-1=43\) है। पहले आधा करें फिर (n) घटाएँ।
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यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+3a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+3a_{n-2}\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=6+3\times2=12\) and \(a_4=12+3\times6=30\). Therefore the correct value is (30).
Step 2
Why this answer is correct
The correct answer is D. (32). \(a_3=6+3\times2=12\) and \(a_4=12+3\times6=30\). Therefore the correct value is (30).
Step 3
Exam Tip
\(a_3=6+3\times2=12\) और \(a_4=12+3\times6=30\) है। इसलिए सही मान (30) है।
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यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+3a_{n-2}\) है तो \(a_3\) क्या होगा?
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+3a_{n-2}\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=6+3\times2=12\). Exam tip: multiply \(a_{n-2}\) by (3) in this two-term rule.
Step 2
Why this answer is correct
The correct answer is B. (12). \(a_3=6+3\times2=12\). Exam tip: multiply \(a_{n-2}\) by (3) in this two-term rule.
Step 3
Exam Tip
\(a_3=6+3\times2=12\) है। दो-पद नियम में \(a_{n-2}\) को (3) से गुणा करें।
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यदि \(a_1=5\) और (a_{n+1}=a_n+(-1)^n) है तो \(a_5\) क्या होगा?
If \(a_1=5\) and (a_{n+1}=a_n+(-1)^n), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,4,5,4,5), so \(a_5=5\). Exam tip: the sign of ((-1)^n) changes with even and odd (n).
Step 2
Why this answer is correct
The correct answer is C. (5). The terms are (5,4,5,4,5), so \(a_5=5\). Exam tip: the sign of ((-1)^n) changes with even and odd (n).
Step 3
Exam Tip
पद (5,4,5,4,5) हैं इसलिए \(a_5=5\) है। ((-1)^n) में सम और विषम (n) का चिह्न बदलता है।
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यदि \(a_1=4\) और (a_{n+1}=a_n+2(-1)^n) है तो \(a_4\) क्या होगा?
If \(a_1=4\) and (a_{n+1}=a_n+2(-1)^n), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,2,4,2), so \(a_4=2\). The correct option should be (2).
Step 2
Why this answer is correct
The correct answer is B. (4). The terms are (4,2,4,2), so \(a_4=2\). The correct option should be (2).
Step 3
Exam Tip
पद (4,2,4,2) हैं इसलिए \(a_4=2\) है। सही विकल्प (2) होना चाहिए।
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यदि \(a_1=4\) और (a_{n+1}=a_n+2(-1)^n) है तो \(a_3\) क्या होगा?
If \(a_1=4\) and (a_{n+1}=a_n+2(-1)^n), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,2,4), so \(a_3=4\). Exam tip: check the sign of ((-1)^n) at every step.
Step 2
Why this answer is correct
The correct answer is B. (4). The terms are (4,2,4), so \(a_3=4\). Exam tip: check the sign of ((-1)^n) at every step.
Step 3
Exam Tip
पद (4,2,4) हैं इसलिए \(a_3=4\) है। ((-1)^n) के चिह्न को हर चरण में जाँचें।
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यदि \(a_1=1\) और \(a_{n+1}=a_n+2^n\) है तो \(a_5\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=a_n+2^n\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,7,15,31), so \(a_5=31\). Exam tip: add (2,4,8,16) in order.
Step 2
Why this answer is correct
The correct answer is C. (31). The terms are (1,3,7,15,31), so \(a_5=31\). Exam tip: add (2,4,8,16) in order.
Step 3
Exam Tip
पद (1,3,7,15,31) हैं इसलिए \(a_5=31\) है। \(2^n\) के मान (2,4,8,16) क्रम से जोड़ें।
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यदि \(a_1=100\) और \(a_{n+1}=a_n-2^n\) है तो \(a_4\) क्या होगा?
If \(a_1=100\) and \(a_{n+1}=a_n-2^n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (100,98,94,86), so \(a_4=86\). Exam tip: subtract the values of \(2^n\) in order.
Step 2
Why this answer is correct
The correct answer is C. (86). The terms are (100,98,94,86), so \(a_4=86\). Exam tip: subtract the values of \(2^n\) in order.
Step 3
Exam Tip
पद (100,98,94,86) हैं इसलिए \(a_4=86\) है। \(2^n\) के मान क्रम से घटाएँ।
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यदि \(a_1=3\) और (a_{n+1}=a_n+n(n+1)) है तो \(a_4\) क्या होगा?
If \(a_1=3\) and (a_{n+1}=a_n+n(n+1)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,5,11,23), so \(a_4=23\). Exam tip: (n(n+1)) gives (2,6,12).
Step 2
Why this answer is correct
The correct answer is D. (23). The terms are (3,5,11,23), so \(a_4=23\). Exam tip: (n(n+1)) gives (2,6,12).
Step 3
Exam Tip
पद (3,5,11,23) हैं इसलिए \(a_4=23\) है। (n(n+1)) का मान (2,6,12) बनता है।
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यदि \(a_1=60\) और (a_{n+1}=a_n-n(n+1)) है तो \(a_4\) क्या होगा?
If \(a_1=60\) and (a_{n+1}=a_n-n(n+1)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (60,58,52,40), so \(a_4=40\). Exam tip: calculate the product and then subtract.
Step 2
Why this answer is correct
The correct answer is A. (40). The terms are (60,58,52,40), so \(a_4=40\). Exam tip: calculate the product and then subtract.
Step 3
Exam Tip
पद (60,58,52,40) हैं इसलिए \(a_4=40\) है। गुणनफल निकालकर घटाएँ।
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यदि \(a_1=2\) और \(a_{n+1}=a_n+2a_1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n+2a_1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
Here \(2a_1=4\) is added each time, so the terms are (2,6,10,14). Exam tip: \(a_1\) stays constant.
Step 2
Why this answer is correct
The correct answer is C. (14). Here \(2a_1=4\) is added each time, so the terms are (2,6,10,14). Exam tip: \(a_1\) stays constant.
Step 3
Exam Tip
यहाँ \(2a_1=4\) हर बार जुड़ता है इसलिए पद (2,6,10,14) हैं। \(a_1\) स्थिर रहता है।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+a_1+n\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+a_1+n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=6+6+1=13\) and \(a_3=13+6+2=21\). Exam tip: \(a_1\) is fixed while (n) changes.
Step 2
Why this answer is correct
The correct answer is C. (21). \(a_2=6+6+1=13\) and \(a_3=13+6+2=21\). Exam tip: \(a_1\) is fixed while (n) changes.
Step 3
Exam Tip
\(a_2=6+6+1=13\) और \(a_3=13+6+2=21\) है। \(a_1\) स्थिर और (n) बदलता है।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+n\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+n\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=6\), \(a_4=10\), and \(a_5=15\). The correct option should include (15).
Step 2
Why this answer is correct
The correct answer is B. (14). \(a_3=6\), \(a_4=10\), and \(a_5=15\). The correct option should include (15).
Step 3
Exam Tip
\(a_3=6\), \(a_4=10\) और \(a_5=15\) नहीं बल्कि \(a_5=15\) है। विकल्पों में (15) होना चाहिए।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=3+3=6\) and \(a_4=6+4=10\). Exam tip: this rule adds the current (n).
Step 2
Why this answer is correct
The correct answer is C. (10). \(a_3=3+3=6\) and \(a_4=6+4=10\). Exam tip: this rule adds the current (n).
Step 3
Exam Tip
\(a_3=3+3=6\) और \(a_4=6+4=10\) है। इस नियम में वर्तमान (n) जोड़ा जाता है।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+4\) है तो \(a_7\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=a_n+4\), what is \(a_7\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,9,13,17,21,25,29), so \(a_7=29\). Exam tip: add (4) six times for \(a_7\).
Step 2
Why this answer is correct
The correct answer is B. (29). The terms are (5,9,13,17,21,25,29), so \(a_7=29\). Exam tip: add (4) six times for \(a_7\).
Step 3
Exam Tip
पद (5,9,13,17,21,25,29) हैं इसलिए \(a_7=29\) है। recursive rule में (6) बार (4) जोड़ना होगा।
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यदि \(a_1=12\) और \(a_{n+1}=a_n+6\) है तो कौन सा पद (42) है?
If \(a_1=12\) and \(a_{n+1}=a_n+6\), which term is (42)?
Explanation opens after your attempt
Correct Answer
B. (6)वाँ/(6)th
Step 1
Concept
The terms are (12,18,24,30,36,42), so (42) is the sixth term. Exam tip: write terms with their positions.
Step 2
Why this answer is correct
The correct answer is B. (6)वाँ / (6)th. The terms are (12,18,24,30,36,42), so (42) is the sixth term. Exam tip: write terms with their positions.
Step 3
Exam Tip
पद (12,18,24,30,36,42) हैं इसलिए (42) छठा पद है। पदों को क्रमांक के साथ लिखें।
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यदि \(a_1=3\) और \(a_{n+1}=2a_n+2\) है तो \(a_4-a_2\) का मान क्या होगा?
If \(a_1=3\) and \(a_{n+1}=2a_n+2\), what is the value of \(a_4-a_2\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,8,18,38), so \(a_4-a_2=30\). The correct difference should be (30).
Step 2
Why this answer is correct
The correct answer is C. (24). The terms are (3,8,18,38), so \(a_4-a_2=30\). The correct difference should be (30).
Step 3
Exam Tip
पद (3,8,18,38) हैं इसलिए \(a_4-a_2=38-8=30\) है। सही अंतर (30) होना चाहिए।
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यदि \(a_1=3\) और \(a_{n+1}=2a_n+2\) है तो \(a_3-a_2\) का मान क्या होगा?
If \(a_1=3\) and \(a_{n+1}=2a_n+2\), what is the value of \(a_3-a_2\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,8,18), so \(a_3-a_2=18-8=10\). Exam tip: find both terms first and then subtract.
Step 2
Why this answer is correct
The correct answer is B. (10). The terms are (3,8,18), so \(a_3-a_2=18-8=10\). Exam tip: find both terms first and then subtract.
Step 3
Exam Tip
पद (3,8,18) हैं इसलिए \(a_3-a_2=18-8=10\) है। पहले दोनों पद निकालें फिर घटाएँ।
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=a_{n-1}+a_{n-2}+1\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=a_{n-1}+a_{n-2}+1\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,8,14,23), so \(a_5=23\). Include the extra (1) at each step.
Step 2
Why this answer is correct
The correct answer is C. (22). The terms are (2,5,8,14,23), so \(a_5=23\). Include the extra (1) at each step.
Step 3
Exam Tip
पद (2,5,8,14,23) नहीं बल्कि \(a_5=23\) है। जोड़ में अतिरिक्त (1) हर चरण शामिल करें।
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=a_{n-1}+a_{n-2}+1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=a_{n-1}+a_{n-2}+1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=5+2+1=8\) and \(a_4=8+5+1=14\). Exam tip: add (1) along with the previous two terms.
Step 2
Why this answer is correct
The correct answer is D. (14). \(a_3=5+2+1=8\) and \(a_4=8+5+1=14\). Exam tip: add (1) along with the previous two terms.
Step 3
Exam Tip
\(a_3=5+2+1=8\) और \(a_4=8+5+1=14\) है। पिछले दो पदों के साथ (1) भी जोड़ें।
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यदि \(a_1=4\) और \(a_{n+1}=3a_n-2\) है तो \(a_3\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=3a_n-2\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,10,28), so \(a_3=28\). Exam tip: multiply by (3) first and then subtract (2).
Step 2
Why this answer is correct
The correct answer is B. (28). The terms are (4,10,28), so \(a_3=28\). Exam tip: multiply by (3) first and then subtract (2).
Step 3
Exam Tip
पद (4,10,28) हैं इसलिए \(a_3=28\) है। पहले (3) से गुणा करें फिर (2) घटाएँ।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+5n-2\) है तो \(a_4\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+5n-2\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (6,9,17,30), so \(a_4=30\). The correct option should include (30).
Step 2
Why this answer is correct
The correct answer is B. (27). The terms are (6,9,17,30), so \(a_4=30\). The correct option should include (30).
Step 3
Exam Tip
पद (6,9,17,30) नहीं बल्कि \(a_4=30\) है। सही विकल्प में (30) होना चाहिए।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+5n-2\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+5n-2\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (6,9,17), so \(a_3=17\). Exam tip: (5n-2) changes at each step.
Step 2
Why this answer is correct
The correct answer is B. (17). The terms are (6,9,17), so \(a_3=17\). Exam tip: (5n-2) changes at each step.
Step 3
Exam Tip
पद (6,9,17) हैं इसलिए \(a_3=17\) है। (5n-2) का मान हर चरण में बदलता है।
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यदि \(a_1=1\) और \(a_{n+1}=a_n+n^2+n\) है तो \(a_4\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=a_n+n^2+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,9,21), so \(a_4=21\). The values of \(n^2+n\) are (2,6,12).
Step 2
Why this answer is correct
The correct answer is C. (23). The terms are (1,3,9,21), so \(a_4=21\). The values of \(n^2+n\) are (2,6,12).
Step 3
Exam Tip
पद (1,3,9,21) नहीं बल्कि \(a_4=21\) है। \(n^2+n\) के मान (2,6,12) हैं।
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यदि \(a_1=1\) और \(a_{n+1}=a_n+n^2+n\) है तो \(a_3\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=a_n+n^2+n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,9), so \(a_3=9\). Exam tip: calculate \(n^2+n\) correctly before adding.
Step 2
Why this answer is correct
The correct answer is B. (9). The terms are (1,3,9), so \(a_3=9\). Exam tip: calculate \(n^2+n\) correctly before adding.
Step 3
Exam Tip
पद (1,3,9) हैं इसलिए \(a_3=9\) है। \(n^2+n\) को जोड़ने से पहले सही निकालें।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+2a_n\) है तो \(a_3\) क्या होगा?
If \(a_1=9\) and \(a_{n+1}=a_n+2a_n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
This rule is the same as \(a_{n+1}=3a_n\). The terms are (9,27,81), so \(a_3=81\).
Step 2
Why this answer is correct
The correct answer is D. (81). This rule is the same as \(a_{n+1}=3a_n\). The terms are (9,27,81), so \(a_3=81\).
Step 3
Exam Tip
यह नियम \(a_{n+1}=3a_n\) के समान है। पद (9,27,81) हैं इसलिए \(a_3=81\) है।
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यदि \(a_1=12\) और \(a_{n+1}=a_n+\frac{a_n}{2}\) है तो \(a_3\) क्या होगा?
If \(a_1=12\) and \(a_{n+1}=a_n+\frac{a_n}{2}\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (12,18,27), so \(a_3=27\). Exam tip: the rule means taking one and a half times the previous term.
Step 2
Why this answer is correct
The correct answer is B. (27). The terms are (12,18,27), so \(a_3=27\). Exam tip: the rule means taking one and a half times the previous term.
Step 3
Exam Tip
पद (12,18,27) हैं इसलिए \(a_3=27\) है। नियम का अर्थ पिछले पद का डेढ़ गुना लेना है।
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