यदि \(a_1=4\) और \(a_{n+1}=a_n+3n\) है तो \(a_4\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+3n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,7,13,22), so \(a_4=22\). Exam tip: add the new value of (3n) at each step.
Step 2
Why this answer is correct
The correct answer is C. (22). The terms are (4,7,13,22), so \(a_4=22\). Exam tip: add the new value of (3n) at each step.
Step 3
Exam Tip
पद (4,7,13,22) हैं इसलिए \(a_4=22\) है। हर चरण में (3n) का नया मान जोड़ें।
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यदि \(a_1=30\) और (a_{n+1}=a_n-(2n+1)) है तो \(a_4\) क्या होगा?
If \(a_1=30\) and (a_{n+1}=a_n-(2n+1)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (30,27,22,15), so \(a_4=15\). Exam tip: calculate (2n+1) correctly before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (15). The terms are (30,27,22,15), so \(a_4=15\). Exam tip: calculate (2n+1) correctly before subtracting.
Step 3
Exam Tip
पद (30,27,22,15) हैं इसलिए \(a_4=15\) है। घटाने से पहले (2n+1) सही निकालें।
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यदि \(a_1=2\) और \(a_{n+1}=2a_n+n\) है तो \(a_5\) का मान क्या होगा?
If \(a_1=2\) and \(a_{n+1}=2a_n+n\), what is the value of \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,12,27,58), so \(a_5=58\). Exam tip: double the previous term first and then add (n).
Step 2
Why this answer is correct
The correct answer is D. (58). The terms are (2,5,12,27,58), so \(a_5=58\). Exam tip: double the previous term first and then add (n).
Step 3
Exam Tip
पद (2,5,12,27,58) हैं इसलिए \(a_5=58\) है। पहले पिछले पद को दोगुना करें फिर (n) जोड़ें।
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यदि \(a_1=6\) और \(a_{n+1}=3a_n-2\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=3a_n-2\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=16\) and \(a_3=46\). Exam tip: multiply by (3) first and then subtract (2).
Step 2
Why this answer is correct
The correct answer is B. (46). \(a_2=16\) and \(a_3=46\). Exam tip: multiply by (3) first and then subtract (2).
Step 3
Exam Tip
\(a_2=16\) और \(a_3=46\) है। पहले (3) से गुणा करें फिर (2) घटाएँ।
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यदि \(a_1=1\) और \(a_{n+1}=a_n+n^2+1\) है तो \(a_4\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=a_n+n^2+1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,8,18), so \(a_4=18\). Exam tip: the value of \(n^2+1\) changes at each step.
Step 2
Why this answer is correct
The correct answer is C. (18). The terms are (1,3,8,18), so \(a_4=18\). Exam tip: the value of \(n^2+1\) changes at each step.
Step 3
Exam Tip
पद (1,3,8,18) हैं इसलिए \(a_4=18\) है। \(n^2+1\) का मान हर चरण में बदलता है।
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यदि \(a_1=50\) और \(a_{n+1}=a_n-n^2\) है तो \(a_5\) क्या होगा?
If \(a_1=50\) and \(a_{n+1}=a_n-n^2\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (50,49,45,36,20), so \(a_5=20\). Exam tip: subtract the squares (1,4,9,16) in order.
Step 2
Why this answer is correct
The correct answer is A. (20). The terms are (50,49,45,36,20), so \(a_5=20\). Exam tip: subtract the squares (1,4,9,16) in order.
Step 3
Exam Tip
पद (50,49,45,36,20) हैं इसलिए \(a_5=20\) है। वर्गों (1,4,9,16) को क्रम से घटाएँ।
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यदि \(a_1=3\), \(a_2=5\) और \(a_n=a_{n-1}+2a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=3\), \(a_2=5\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,5,11,21,43), so \(a_5=43\). The correct option should include (43).
Step 2
Why this answer is correct
The correct answer is C. (31). The terms are (3,5,11,21,43), so \(a_5=43\). The correct option should include (43).
Step 3
Exam Tip
पद (3,5,11,21,43) नहीं बल्कि \(a_5=43\) होता है। सही विकल्प में (43) होना चाहिए।
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यदि \(a_1=3\), \(a_2=5\) और \(a_n=a_{n-1}+2a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=3\), \(a_2=5\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=5+2\times3=11\) and \(a_4=11+2\times5=21\). Exam tip: write positions while using two-term rules.
Step 2
Why this answer is correct
The correct answer is C. (21). \(a_3=5+2\times3=11\) and \(a_4=11+2\times5=21\). Exam tip: write positions while using two-term rules.
Step 3
Exam Tip
\(a_3=5+2\times3=11\) और \(a_4=11+2\times5=21\) है। दो-पद नियम में क्रमांक साथ लिखें।
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यदि \(a_1=4\), \(a_2=9\) और \(a_n=2a_{n-1}-a_{n-2}\) है तो \(a_6\) क्या होगा?
If \(a_1=4\), \(a_2=9\), and \(a_n=2a_{n-1}-a_{n-2}\), what is \(a_6\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,9,14,19,24,29), so \(a_6=29\). Exam tip: this rule keeps the difference constant.
Step 2
Why this answer is correct
The correct answer is C. (29). The terms are (4,9,14,19,24,29), so \(a_6=29\). Exam tip: this rule keeps the difference constant.
Step 3
Exam Tip
पद (4,9,14,19,24,29) हैं इसलिए \(a_6=29\) है। इस नियम में अंतर समान बना रहता है।
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यदि \(a_1=2\) और \(a_{n+1}=a_n+2^n\) है तो \(a_5\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n+2^n\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,4,8,16,32), so \(a_5=32\). Exam tip: add the values of \(2^n\) in order.
Step 2
Why this answer is correct
The correct answer is C. (32). The terms are (2,4,8,16,32), so \(a_5=32\). Exam tip: add the values of \(2^n\) in order.
Step 3
Exam Tip
पद (2,4,8,16,32) हैं इसलिए \(a_5=32\) है। \(2^n\) के मान क्रम से जोड़ें।
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यदि \(a_1=90\) और \(a_{n+1}=a_n-2^n\) है तो \(a_4\) क्या होगा?
If \(a_1=90\) and \(a_{n+1}=a_n-2^n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (90,88,84,76), so \(a_4=76\). Exam tip: subtract (2,4,8) in order.
Step 2
Why this answer is correct
The correct answer is B. (76). The terms are (90,88,84,76), so \(a_4=76\). Exam tip: subtract (2,4,8) in order.
Step 3
Exam Tip
पद (90,88,84,76) हैं इसलिए \(a_4=76\) है। (2,4,8) को क्रम से घटाएँ।
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यदि \(a_1=5\) और (a_{n+1}=a_n+(-1)^{n+1}n) है तो \(a_5\) क्या होगा?
If \(a_1=5\) and (a_{n+1}=a_n+(-1)^{n+1}n), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,6,4,7,3), so \(a_5=3\). The correct option should include (3).
Step 2
Why this answer is correct
The correct answer is C. (7). The terms are (5,6,4,7,3), so \(a_5=3\). The correct option should include (3).
Step 3
Exam Tip
पद (5,6,4,7,3) नहीं बल्कि \(a_5=3\) है। सही विकल्प में (3) होना चाहिए।
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यदि \(a_1=5\) और (a_{n+1}=a_n+(-1)^{n+1}n) है तो \(a_4\) क्या होगा?
If \(a_1=5\) and (a_{n+1}=a_n+(-1)^{n+1}n), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (5,6,4,7), so \(a_4=7\). Exam tip: check the sign of ((-1)^{n+1}) at each step.
Step 2
Why this answer is correct
The correct answer is D. (7). The terms are (5,6,4,7), so \(a_4=7\). Exam tip: check the sign of ((-1)^{n+1}) at each step.
Step 3
Exam Tip
पद (5,6,4,7) हैं इसलिए \(a_4=7\) है। ((-1)^{n+1}) के चिह्न को हर चरण में जाँचें।
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यदि \(a_1=2\) और (a_{n+1}=a_n+n(n+2)) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and (a_{n+1}=a_n+n(n+2)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,13,28), so \(a_4=28\). Add the values (3,8,15) of (n(n+2)).
Step 2
Why this answer is correct
The correct answer is C. (26). The terms are (2,5,13,28), so \(a_4=28\). Add the values (3,8,15) of (n(n+2)).
Step 3
Exam Tip
पद (2,5,13,28) नहीं बल्कि \(a_4=28\) है। (n(n+2)) के मान (3,8,15) जोड़ें।
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यदि \(a_1=2\) और (a_{n+1}=a_n+n(n+2)) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and (a_{n+1}=a_n+n(n+2)), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,13), so \(a_3=13\). Exam tip: calculate the product before adding.
Step 2
Why this answer is correct
The correct answer is B. (13). The terms are (2,5,13), so \(a_3=13\). Exam tip: calculate the product before adding.
Step 3
Exam Tip
पद (2,5,13) हैं इसलिए \(a_3=13\) है। गुणनफल निकालकर जोड़ना चाहिए।
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यदि \(a_1=100\) और (a_{n+1}=a_n-n(n+2)) है तो \(a_4\) क्या होगा?
If \(a_1=100\) and (a_{n+1}=a_n-n(n+2)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (100,97,89,74), so \(a_4=74\). Exam tip: subtract (3,8,15) in order.
Step 2
Why this answer is correct
The correct answer is A. (74). The terms are (100,97,89,74), so \(a_4=74\). Exam tip: subtract (3,8,15) in order.
Step 3
Exam Tip
पद (100,97,89,74) हैं इसलिए \(a_4=74\) है। (3,8,15) को क्रम से घटाएँ।
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यदि \(a_1=7\) और \(a_{n+1}=2a_n+3\) है तो \(a_4\) क्या होगा?
If \(a_1=7\) and \(a_{n+1}=2a_n+3\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (7,17,37,77), so \(a_4=77\). The correct option should include (77).
Step 2
Why this answer is correct
The correct answer is C. (69). The terms are (7,17,37,77), so \(a_4=77\). The correct option should include (77).
Step 3
Exam Tip
पद (7,17,37,77) नहीं बल्कि \(a_4=77\) है। सही विकल्प में (77) होना चाहिए।
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यदि \(a_1=7\) और \(a_{n+1}=2a_n+3\) है तो \(a_3\) क्या होगा?
If \(a_1=7\) and \(a_{n+1}=2a_n+3\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (7,17,37), so \(a_3=37\). Exam tip: double first and then add (3).
Step 2
Why this answer is correct
The correct answer is D. (37). The terms are (7,17,37), so \(a_3=37\). Exam tip: double first and then add (3).
Step 3
Exam Tip
पद (7,17,37) हैं इसलिए \(a_3=37\) है। पहले दोगुना करें फिर (3) जोड़ें।
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यदि \(a_1=8\) और \(a_{n+1}=3a_n+n\) है तो \(a_3\) क्या होगा?
If \(a_1=8\) and \(a_{n+1}=3a_n+n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=3\times8+1=25\) and \(a_3=3\times25+2=77\). Therefore the correct value is (77).
Step 2
Why this answer is correct
The correct answer is C. (79). \(a_2=3\times8+1=25\) and \(a_3=3\times25+2=77\). Therefore the correct value is (77).
Step 3
Exam Tip
\(a_2=3\times8+1=25\) और \(a_3=3\times25+2=77\) है। इसलिए सही मान (77) है।
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यदि \(a_1=8\) और \(a_{n+1}=3a_n+n\) है तो \(a_2\) क्या होगा?
If \(a_1=8\) and \(a_{n+1}=3a_n+n\), what is \(a_2\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=3\times8+1=25\). Exam tip: use (n=1) for the next term.
Step 2
Why this answer is correct
The correct answer is B. (25). \(a_2=3\times8+1=25\). Exam tip: use (n=1) for the next term.
Step 3
Exam Tip
\(a_2=3\times8+1=25\) है। अगले पद के लिए (n=1) रखें।
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यदि \(a_1=3\) और (a_{n+1}=a_n+\frac{n(n+1)}{2}) है तो \(a_5\) क्या होगा?
If \(a_1=3\) and (a_{n+1}=a_n+\frac{n(n+1)}{2}), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,4,7,13,23), so \(a_5=23\). Exam tip: add triangular increments (1,3,6,10) in order.
Step 2
Why this answer is correct
The correct answer is B. (23). The terms are (3,4,7,13,23), so \(a_5=23\). Exam tip: add triangular increments (1,3,6,10) in order.
Step 3
Exam Tip
पद (3,4,7,13,23) हैं इसलिए \(a_5=23\) है। त्रिभुजीय जोड़ (1,3,6,10) क्रम से जोड़ें।
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यदि \(a_1=70\) और (a_{n+1}=a_n-\frac{n(n+1)}{2}) है तो \(a_4\) क्या होगा?
If \(a_1=70\) and (a_{n+1}=a_n-\frac{n(n+1)}{2}), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (70,69,66,60), so \(a_4=60\). Exam tip: subtract (1,3,6) in order.
Step 2
Why this answer is correct
The correct answer is B. (60). The terms are (70,69,66,60), so \(a_4=60\). Exam tip: subtract (1,3,6) in order.
Step 3
Exam Tip
पद (70,69,66,60) हैं इसलिए \(a_4=60\) है। (1,3,6) को क्रम से घटाएँ।
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यदि \(a_1=10\) और \(a_{n+1}=\frac{a_n}{2}+2n\) है तो \(a_3\) क्या होगा?
If \(a_1=10\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=5+2=7\) and \(a_3=\frac{7}{2}+4=7.5\). None of the options is correct.
Step 2
Why this answer is correct
The correct answer is C. (10). \(a_2=5+2=7\) and \(a_3=\frac{7}{2}+4=7.5\). None of the options is correct.
Step 3
Exam Tip
\(a_2=5+2=7\) और \(a_3=\frac{7}{2}+4=7.5\) है। दिए गए विकल्पों में सही मान नहीं है।
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यदि \(a_1=12\) और \(a_{n+1}=\frac{a_n}{2}+2n\) है तो \(a_2\) क्या होगा?
If \(a_1=12\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_2\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=\frac{12}{2}+2=8\). Exam tip: halve first and then add (2n).
Step 2
Why this answer is correct
The correct answer is B. (8). \(a_2=\frac{12}{2}+2=8\). Exam tip: halve first and then add (2n).
Step 3
Exam Tip
\(a_2=\frac{12}{2}+2=8\) है। पहले आधा करें फिर (2n) जोड़ें।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+2a_1+n\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+2a_1+n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=6+12+1=19\) and \(a_3=19+12+2=33\). The correct option should be (33).
Step 2
Why this answer is correct
The correct answer is B. (31). \(a_2=6+12+1=19\) and \(a_3=19+12+2=33\). The correct option should be (33).
Step 3
Exam Tip
\(a_2=6+12+1=19\) और \(a_3=19+12+2=33\) नहीं बल्कि (33) है। सही विकल्प (33) होना चाहिए।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+2a_1+n\) है तो \(a_2\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+2a_1+n\), what is \(a_2\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=6+2\times6+1=19\). Exam tip: \(a_1\) stays fixed while (n) changes.
Step 2
Why this answer is correct
The correct answer is B. (19). \(a_2=6+2\times6+1=19\). Exam tip: \(a_1\) stays fixed while (n) changes.
Step 3
Exam Tip
\(a_2=6+2\times6+1=19\) है। \(a_1\) स्थिर रहता है और (n) बदलता है।
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यदि \(a_1=2\), \(a_2=4\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=4+2+3=9\) and \(a_4=9+4+4=17\). The correct option should include (17).
Step 2
Why this answer is correct
The correct answer is C. (14). \(a_3=4+2+3=9\) and \(a_4=9+4+4=17\). The correct option should include (17).
Step 3
Exam Tip
\(a_3=4+2+3=9\) और \(a_4=9+4+4=17\) है। सही विकल्प में (17) होना चाहिए।
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यदि \(a_1=2\), \(a_2=4\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_3\) क्या होगा?
If \(a_1=2\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=4+2+3=9\). Exam tip: add the current (n) along with the previous two terms.
Step 2
Why this answer is correct
The correct answer is C. (9). \(a_3=4+2+3=9\). Exam tip: add the current (n) along with the previous two terms.
Step 3
Exam Tip
\(a_3=4+2+3=9\) है। इस नियम में पिछले दो पदों के साथ वर्तमान (n) भी जोड़ें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n^2-a_n\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n^2-a_n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=9-3=6\) and \(a_3=36-6=30\). Exam tip: square the previous term and subtract that term.
Step 2
Why this answer is correct
The correct answer is B. (30). \(a_2=9-3=6\) and \(a_3=36-6=30\). Exam tip: square the previous term and subtract that term.
Step 3
Exam Tip
\(a_2=9-3=6\) और \(a_3=36-6=30\) है। पिछले पद का वर्ग लेकर वही पद घटाएँ।
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यदि \(a_1=2\) और \(a_{n+1}=a_n^2+a_n\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n^2+a_n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=4+2=6\) and \(a_3=36+6=42\). Exam tip: square first and then add the previous term.
Step 2
Why this answer is correct
The correct answer is C. (42). \(a_2=4+2=6\) and \(a_3=36+6=42\). Exam tip: square first and then add the previous term.
Step 3
Exam Tip
\(a_2=4+2=6\) और \(a_3=36+6=42\) है। पहले वर्ग करें फिर पिछले पद को जोड़ें।
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यदि \(a_1=4\) और \(a_{n+1}=a_n+3\) है तो \(a_8\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+3\), what is \(a_8\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,7,10,13,16,19,22,25), so \(a_8=25\). Exam tip: add (3) seven times for \(a_8\).
Step 2
Why this answer is correct
The correct answer is B. (25). The terms are (4,7,10,13,16,19,22,25), so \(a_8=25\). Exam tip: add (3) seven times for \(a_8\).
Step 3
Exam Tip
पद (4,7,10,13,16,19,22,25) हैं इसलिए \(a_8=25\) है। \(a_8\) के लिए (7) बार (3) जोड़ें।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+7\) है तो कौन सा पद (51) है?
If \(a_1=9\) and \(a_{n+1}=a_n+7\), which term is (51)?
Explanation opens after your attempt
Correct Answer
B. (7)वाँ/(7)th
Step 1
Concept
The terms are (9,16,23,30,37,44,51), so (51) is the seventh term. Exam tip: write terms with their positions.
Step 2
Why this answer is correct
The correct answer is B. (7)वाँ / (7)th. The terms are (9,16,23,30,37,44,51), so (51) is the seventh term. Exam tip: write terms with their positions.
Step 3
Exam Tip
पद (9,16,23,30,37,44,51) हैं इसलिए (51) सातवाँ पद है। पदों को क्रमांक के साथ लिखें।
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यदि \(a_1=4\) और \(a_{n+1}=2a_n+1\) है तो \(a_4-a_2\) का मान क्या होगा?
If \(a_1=4\) and \(a_{n+1}=2a_n+1\), what is the value of \(a_4-a_2\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (4,9,19,39), so \(a_4-a_2=39-9=30\). Exam tip: find both terms first and then subtract.
Step 2
Why this answer is correct
The correct answer is B. (30). The terms are (4,9,19,39), so \(a_4-a_2=39-9=30\). Exam tip: find both terms first and then subtract.
Step 3
Exam Tip
पद (4,9,19,39) हैं इसलिए \(a_4-a_2=39-9=30\) है। पहले दोनों पद निकालें फिर घटाएँ।
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यदि \(a_1=3\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+2\) है तो \(a_5\) क्या होगा?
If \(a_1=3\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+2\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (3,6,11,19,32), so \(a_5=32\). The correct option should include (32).
Step 2
Why this answer is correct
The correct answer is B. (27). The terms are (3,6,11,19,32), so \(a_5=32\). The correct option should include (32).
Step 3
Exam Tip
पद (3,6,11,19,32) नहीं बल्कि \(a_5=32\) है। सही विकल्प में (32) होना चाहिए।
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यदि \(a_1=3\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+2\) है तो \(a_4\) क्या होगा?
If \(a_1=3\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+2\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=6+3+2=11\) and \(a_4=11+6+2=19\). Exam tip: add the extra (2) at each step.
Step 2
Why this answer is correct
The correct answer is C. (19). \(a_3=6+3+2=11\) and \(a_4=11+6+2=19\). Exam tip: add the extra (2) at each step.
Step 3
Exam Tip
\(a_3=6+3+2=11\) और \(a_4=11+6+2=19\) है। अतिरिक्त (2) हर चरण में जोड़ें।
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यदि \(a_1=5\) और \(a_{n+1}=4a_n-1\) है तो \(a_3\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=4a_n-1\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=4\times5-1=19\) and \(a_3=4\times19-1=75\). Exam tip: subtract (1) after multiplication.
Step 2
Why this answer is correct
The correct answer is B. (75). \(a_2=4\times5-1=19\) and \(a_3=4\times19-1=75\). Exam tip: subtract (1) after multiplication.
Step 3
Exam Tip
\(a_2=4\times5-1=19\) और \(a_3=4\times19-1=75\) है। गुणा के बाद (1) घटाएँ।
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यदि \(a_1=2\) और \(a_{n+1}=a_n+5n-1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n+5n-1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,6,15,29), so \(a_4=29\). Exam tip: add the changing values of (5n-1).
Step 2
Why this answer is correct
The correct answer is D. (29). The terms are (2,6,15,29), so \(a_4=29\). Exam tip: add the changing values of (5n-1).
Step 3
Exam Tip
पद (2,6,15,29) हैं इसलिए \(a_4=29\) है। (5n-1) के बदलते मान जोड़ें।
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यदि \(a_1=120\) और (a_{n+1}=a_n-(3n+2)) है तो \(a_4\) क्या होगा?
If \(a_1=120\) and (a_{n+1}=a_n-(3n+2)), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (120,115,107,96), so \(a_4=96\). Exam tip: calculate (3n+2) before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (96). The terms are (120,115,107,96), so \(a_4=96\). Exam tip: calculate (3n+2) before subtracting.
Step 3
Exam Tip
पद (120,115,107,96) हैं इसलिए \(a_4=96\) है। घटाने से पहले (3n+2) निकालें।
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यदि \(a_1=2\) और \(a_{n+1}=a_n+n^2+n+1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n+n^2+n+1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,12,25), so \(a_4=25\). The correct option should include (25).
Step 2
Why this answer is correct
The correct answer is B. (23). The terms are (2,5,12,25), so \(a_4=25\). The correct option should include (25).
Step 3
Exam Tip
पद (2,5,12,25) नहीं बल्कि \(a_4=25\) है। सही विकल्प में (25) होना चाहिए।
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यदि \(a_1=2\) और \(a_{n+1}=a_n+n^2+n+1\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n+n^2+n+1\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,12), so \(a_3=12\). Exam tip: calculate \(n^2+n+1\) correctly before adding.
Step 2
Why this answer is correct
The correct answer is B. (12). The terms are (2,5,12), so \(a_3=12\). Exam tip: calculate \(n^2+n+1\) correctly before adding.
Step 3
Exam Tip
पद (2,5,12) हैं इसलिए \(a_3=12\) है। \(n^2+n+1\) को सही निकालकर जोड़ें।
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यदि \(a_1=16\) और \(a_{n+1}=a_n+\frac{a_n}{4}\) है तो \(a_3\) क्या होगा?
If \(a_1=16\) and \(a_{n+1}=a_n+\frac{a_n}{4}\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (16,20,25), so \(a_3=25\). Exam tip: the rule means taking \(\frac{5}{4}\) of the previous term.
Step 2
Why this answer is correct
The correct answer is C. (25). The terms are (16,20,25), so \(a_3=25\). Exam tip: the rule means taking \(\frac{5}{4}\) of the previous term.
Step 3
Exam Tip
पद (16,20,25) हैं इसलिए \(a_3=25\) है। नियम का अर्थ पिछले पद का \(\frac{5}{4}\) लेना है।
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यदि \(a_1=4\) और \(a_{n+1}=a_n+2a_n\) है तो \(a_4\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+2a_n\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
This rule is \(a_{n+1}=3a_n\), and the terms are (4,12,36,108). Exam tip: simplify the rule first.
Step 2
Why this answer is correct
The correct answer is C. (108). This rule is \(a_{n+1}=3a_n\), and the terms are (4,12,36,108). Exam tip: simplify the rule first.
Step 3
Exam Tip
यह नियम \(a_{n+1}=3a_n\) है और पद (4,12,36,108) हैं। नियम को पहले सरल करना अच्छा तरीका है।
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यदि \(a_1=1\), \(a_2=2\) और \(a_n=3a_{n-1}-2a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=1\), \(a_2=2\), and \(a_n=3a_{n-1}-2a_{n-2}\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (1,2,4,8,16), so \(a_5=16\). None of the listed options is correct.
Step 2
Why this answer is correct
The correct answer is A. (5). The terms are (1,2,4,8,16), so \(a_5=16\). None of the listed options is correct.
Step 3
Exam Tip
पद (1,2,4,8,16) नहीं बल्कि \(a_5=16\) है। दिए गए विकल्पों में सही मान नहीं है।
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यदि \(a_1=1\), \(a_2=2\) और \(a_n=3a_{n-1}-2a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=1\), \(a_2=2\), and \(a_n=3a_{n-1}-2a_{n-2}\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=3\times2-2\times1=4\) and \(a_4=3\times4-2\times2=8\). Exam tip: use both previous terms in the rule.
Step 2
Why this answer is correct
The correct answer is B. (8). \(a_3=3\times2-2\times1=4\) and \(a_4=3\times4-2\times2=8\). Exam tip: use both previous terms in the rule.
Step 3
Exam Tip
\(a_3=3\times2-2\times1=4\) और \(a_4=3\times4-2\times2=8\) है। नियम में दोनों पिछले पदों का उपयोग करें।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+2n-2\) है तो \(a_5\) क्या होगा?
If \(a_1=9\) and \(a_{n+1}=a_n+2n-2\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (9,9,11,15,21), so \(a_5=21\). The correct option should include (21).
Step 2
Why this answer is correct
The correct answer is C. (25). The terms are (9,9,11,15,21), so \(a_5=21\). The correct option should include (21).
Step 3
Exam Tip
पद (9,9,11,15,21) नहीं बल्कि \(a_5=21\) है। सही विकल्प में (21) होना चाहिए।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+2n-2\) है तो \(a_4\) क्या होगा?
If \(a_1=9\) and \(a_{n+1}=a_n+2n-2\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
The terms are (9,9,11,15), so \(a_4=15\). Exam tip: (2n-2) changes at each step.
Step 2
Why this answer is correct
The correct answer is B. (15). The terms are (9,9,11,15), so \(a_4=15\). Exam tip: (2n-2) changes at each step.
Step 3
Exam Tip
पद (9,9,11,15) हैं इसलिए \(a_4=15\) है। (2n-2) का मान हर चरण में बदलता है।
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यदि \(a_1=6\), \(a_2=10\) और \(a_n=2a_{n-1}+a_{n-2}-n\) है तो \(a_3\) क्या होगा?
If \(a_1=6\), \(a_2=10\), and \(a_n=2a_{n-1}+a_{n-2}-n\), what is \(a_3\)?
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times10+6-3=23\). Exam tip: subtract the current (n) in this two-term rule.
Step 2
Why this answer is correct
The correct answer is B. (23). \(a_3=2\times10+6-3=23\). Exam tip: subtract the current (n) in this two-term rule.
Step 3
Exam Tip
\(a_3=2\times10+6-3=23\) है। दो-पद नियम में वर्तमान (n) भी घटाएँ।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+\frac{n}{2}\) है तो \(a_5\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=a_n+\frac{n}{2}\), what is \(a_5\)?
Explanation opens after your attempt
Step 1
Concept
\(a_5=5+\frac{1+2+3+4}{2}=10\). Exam tip: add the numerators first in fractional increments.
Step 2
Why this answer is correct
The correct answer is B. (10). \(a_5=5+\frac{1+2+3+4}{2}=10\). Exam tip: add the numerators first in fractional increments.
Step 3
Exam Tip
\(a_5=5+\frac{1+2+3+4}{2}=10\) है। भिन्न जोड़ में अंशों को पहले जोड़ें।
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यदि \(a_1=30\) और \(a_{n+1}=a_n-\frac{n}{2}\) है तो \(a_4\) क्या होगा?
If \(a_1=30\) and \(a_{n+1}=a_n-\frac{n}{2}\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_4=30-\frac{1+2+3}{2}=27\). Exam tip: find the total subtraction first with fractions.
Step 2
Why this answer is correct
The correct answer is B. (27). \(a_4=30-\frac{1+2+3}{2}=27\). Exam tip: find the total subtraction first with fractions.
Step 3
Exam Tip
\(a_4=30-\frac{1+2+3}{2}=27\) है। भिन्न घटाते समय कुल घटाव पहले निकालें।
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यदि \(a_1=2\) और \(a_{n+1}=n a_n+1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=n a_n+1\), what is \(a_4\)?
Explanation opens after your attempt
Step 1
Concept
\(a_2=1\times2+1=3\), \(a_3=2\times3+1=7\), and \(a_4=3\times7+1=22\). The correct option should include (22).
Step 2
Why this answer is correct
The correct answer is B. (16). \(a_2=1\times2+1=3\), \(a_3=2\times3+1=7\), and \(a_4=3\times7+1=22\). The correct option should include (22).
Step 3
Exam Tip
\(a_2=1\times2+1=3\), \(a_3=2\times3+1=7\) और \(a_4=3\times7+1=22\) है। सही विकल्प में (22) होना चाहिए।
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