Level 46 • 50/50 questions • 35 seconds per question.
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If \(a_1=5\) and \(a_{n+1}=a_n+2n+2\), what is \(a_5\)?
C. (33)
पद (5,9,15,23,33) हैं इसलिए \(a_5=33\) है। (2n+2) का मान हर चरण में बदलता है। / The terms are (5,9,15,23,33), so \(a_5=33\). Exam tip: the value of (2n+2) changes at each step.
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If \(a_1=60\) and (a_{n+1}=a_n-(3n+1)), what is \(a_4\)?
B. (39)
पद (60,56,49,39) हैं इसलिए \(a_4=39\) है। घटाने से पहले (3n+1) सही निकालें। / The terms are (60,56,49,39), so \(a_4=39\). Exam tip: calculate (3n+1) correctly before subtracting.
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If \(a_1=3\) and \(a_{n+1}=2a_n+n+1\), what is the value of \(a_4\)?
C. (43)
पद (3,8,20,43) हैं इसलिए \(a_4=43\) है। पहले पिछले पद को दोगुना करें फिर (n+1) जोड़ें। / The terms are (3,8,20,43), so \(a_4=43\). Exam tip: double the previous term first and then add (n+1).
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If \(a_1=7\) and \(a_{n+1}=3a_n-2n\), what is \(a_3\)?
D. (57)
\(a_2=3\times7-2=19\) और \(a_3=3\times19-4=53\) नहीं बल्कि \(a_3=53\) है। सही गणना में (n=2) पर (4) घटता है। / \(a_2=3\times7-2=19\) and \(a_3=3\times19-4=53\). Exam tip: when (n=2), subtract (4).
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If \(a_1=7\) and \(a_{n+1}=3a_n-2n\), what is \(a_2\)?
B. (19)
\(a_2=3\times7-2\times1=19\) है। अगले पद के लिए (n=1) रखें। / \(a_2=3\times7-2\times1=19\). Exam tip: use (n=1) for the next term.
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If \(a_1=2\), \(a_2=5\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_5\)?
B. (27)
पद (2,5,9,19,37) नहीं हैं क्योंकि \(a_5=19+2\times9=37\) होगा। इसलिए सही मान (37) है। / The terms give \(a_3=9\), \(a_4=19\), and \(a_5=37\). Exam tip: multiply \(a_{n-2}\) by (2) before adding.
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If \(a_1=2\), \(a_2=5\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_4\)?
B. (19)
\(a_3=5+2\times2=9\) और \(a_4=9+2\times5=19\) है। दो-पद नियम में क्रमांक साथ लिखें। / \(a_3=5+2\times2=9\) and \(a_4=9+2\times5=19\). Exam tip: write positions while using two-term rules.
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If \(a_1=4\), \(a_2=10\), and \(a_n=2a_{n-1}-a_{n-2}\), what is \(a_6\)?
D. (34)
पद (4,10,16,22,28,34) हैं इसलिए \(a_6=34\) है। यह नियम समान अंतर बनाए रखता है। / The terms are (4,10,16,22,28,34), so \(a_6=34\). Exam tip: this rule preserves a constant difference.
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If \(a_1=6\) and \(a_{n+1}=a_n+n^2+2n\), what is \(a_4\)?
C. (32)
पद (6,9,17,32) हैं इसलिए \(a_4=32\) है। \(n^2+2n\) का मान हर बार नया निकालें। / The terms are (6,9,17,32), so \(a_4=32\). Exam tip: calculate the new value of \(n^2+2n\) each time.
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If \(a_1=90\) and (a_{n+1}=a_n-\(n^2+n\)), what is \(a_4\)?
B. (70)
पद (90,88,82,70) हैं इसलिए \(a_4=70\) है। \(n^2+n\) के मान (2,6,12) क्रम से घटाएँ। / The terms are (90,88,82,70), so \(a_4=70\). Exam tip: subtract (2,6,12) in order.
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If \(a_1=1\) and \(a_{n+1}=a_n+3^n\), what is \(a_4\)?
D. (40)
पद (1,4,13,40) हैं इसलिए \(a_4=40\) है। \(3^n\) के मान (3,9,27) जोड़ें। / The terms are (1,4,13,40), so \(a_4=40\). Exam tip: add (3,9,27), the values of \(3^n\).
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If \(a_1=100\) and \(a_{n+1}=a_n-3^n\), what is \(a_4\)?
A. (61)
पद (100,97,88,61) हैं इसलिए \(a_4=61\) है। (3,9,27) को क्रम से घटाएँ। / The terms are (100,97,88,61), so \(a_4=61\). Exam tip: subtract (3,9,27) in order.
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If \(a_1=8\) and (a_{n+1}=a_n+2(-1)^n+n), what is \(a_4\)?
B. (11)
पद (8,7,11,12) हैं इसलिए \(a_4=12\) है। चिह्न बदलने वाले भाग और (n) दोनों देखें। / The terms are (8,7,11,12), so \(a_4=12\). Exam tip: track both the alternating sign part and (n).
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If \(a_1=8\) and (a_{n+1}=a_n+2(-1)^n+n), what is \(a_3\)?
C. (11)
\(a_2=8-2+1=7\) और \(a_3=7+2+2=11\) है। ((-1)^n) का चिह्न हर चरण में बदलता है। / \(a_2=8-2+1=7\) and \(a_3=7+2+2=11\). Exam tip: the sign of ((-1)^n) changes at each step.
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If \(a_1=3\) and (a_{n+1}=a_n+n(n+3)), what is \(a_4\)?
D. (39)
पद (3,7,17,35) नहीं बल्कि \(a_4=35\) है। (n(n+3)) के मान (4,10,18) जोड़ें। / The terms are (3,7,17,35), so \(a_4=35\). Exam tip: add (4,10,18), the values of (n(n+3)).
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If \(a_1=3\) and (a_{n+1}=a_n+n(n+3)), what is \(a_3\)?
B. (17)
पद (3,7,17) हैं इसलिए \(a_3=17\) है। गुणनफल निकालकर जोड़ें। / The terms are (3,7,17), so \(a_3=17\). Exam tip: calculate the product before adding.
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If \(a_1=120\) and (a_{n+1}=a_n-n(n+3)), what is \(a_4\)?
A. (88)
पद (120,116,106,88) हैं इसलिए \(a_4=88\) है। (4,10,18) को क्रम से घटाएँ। / The terms are (120,116,106,88), so \(a_4=88\). Exam tip: subtract (4,10,18) in order.
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If \(a_1=4\) and \(a_{n+1}=2a_n+5\), what is \(a_4\)?
A. (61)
पद (4,13,31,67) नहीं बल्कि \(a_4=67\) है। सही विकल्प में (67) होना चाहिए। / The terms are (4,13,31,67), so \(a_4=67\). The correct option should include (67).
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If \(a_1=4\) and \(a_{n+1}=2a_n+5\), what is \(a_3\)?
C. (31)
पद (4,13,31) हैं इसलिए \(a_3=31\) है। पहले दोगुना करें फिर (5) जोड़ें। / The terms are (4,13,31), so \(a_3=31\). Exam tip: double first and then add (5).
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If \(a_1=5\) and \(a_{n+1}=3a_n+n+2\), what is \(a_2\)?
B. (18)
\(a_2=3\times5+1+2=18\) है। अगले पद के लिए (n=1) रखें। / \(a_2=3\times5+1+2=18\). Exam tip: use (n=1) for the next term.
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If \(a_1=5\) and \(a_{n+1}=3a_n+n+2\), what is \(a_3\)?
C. (58)
\(a_2=18\) और \(a_3=3\times18+2+2=58\) है। (n) का मान बदलना न भूलें। / \(a_2=18\) and \(a_3=3\times18+2+2=58\). Exam tip: do not forget to change (n).
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If \(a_1=2\) and (a_{n+1}=a_n+\frac{n(n+1)}{2}+1), what is \(a_5\)?
C. (28)
पद (2,4,8,15,26) नहीं बल्कि \(a_5=26\) है। (2,4,7,11) जैसे बढ़ते जोड़ ध्यान से जोड़ें। / The terms are (2,4,8,15,26), so \(a_5=26\). Exam tip: add the increasing increments carefully.
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If \(a_1=2\) and (a_{n+1}=a_n+\frac{n(n+1)}{2}+1), what is \(a_4\)?
B. (15)
पद (2,4,8,15) हैं इसलिए \(a_4=15\) है। त्रिभुजीय संख्या में (1) जोड़कर अगला जोड़ बनता है। / The terms are (2,4,8,15), so \(a_4=15\). Exam tip: the increment is a triangular number plus (1).
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If \(a_1=80\) and (a_{n+1}=a_n-\frac{n(n+1)}{2}-1), what is \(a_4\)?
A. (69)
पद (80,78,74,67) नहीं बल्कि \(a_4=67\) है। घटाव (2,4,7) क्रम से होता है। / The terms are (80,78,74,67), so \(a_4=67\). Exam tip: the subtractions are (2,4,7) in order.
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If \(a_1=80\) and (a_{n+1}=a_n-\frac{n(n+1)}{2}-1), what is \(a_3\)?
B. (74)
पद (80,78,74) हैं इसलिए \(a_3=74\) है। घटाने से पहले पूरा मान निकालें। / The terms are (80,78,74), so \(a_3=74\). Exam tip: calculate the full subtraction first.
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If \(a_1=14\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_3\)?
C. (11)
\(a_2=7+2=9\) और \(a_3=\frac{9}{2}+4=8.5\) है। इसलिए पूर्णांक विकल्पों में सही मान नहीं है। / \(a_2=7+2=9\) and \(a_3=\frac{9}{2}+4=8.5\). So no integer option is correct.
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If \(a_1=16\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_2\)?
B. (10)
\(a_2=\frac{16}{2}+2=10\) है। पहले आधा करें फिर (2n) जोड़ें। / \(a_2=\frac{16}{2}+2=10\). Exam tip: halve first and then add (2n).
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If \(a_1=4\) and \(a_{n+1}=a_n+3a_1+n\), what is \(a_3\)?
D. (31)
\(a_2=4+12+1=17\) और \(a_3=17+12+2=31\) है। \(a_1\) स्थिर रहता है और (n) बदलता है। / \(a_2=4+12+1=17\) and \(a_3=17+12+2=31\). Exam tip: \(a_1\) stays fixed while (n) changes.
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If \(a_1=3\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_3\)?
B. (13)
\(a_3=4+3+2\times3=13\) है। पिछले दो पदों के साथ वर्तमान (2n) जोड़ें। / \(a_3=4+3+2\times3=13\). Exam tip: add current (2n) with the previous two terms.
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If \(a_1=3\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_4\)?
B. (25)
\(a_3=13\) और \(a_4=13+4+8=25\) है। दो-पद नियम में वर्तमान (n) सही रखें। / \(a_3=13\) and \(a_4=13+4+8=25\). Exam tip: use the correct current (n) in a two-term rule.
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If \(a_1=4\) and \(a_{n+1}=a_n^2-2a_n\), what is \(a_3\)?
B. (32)
\(a_2=16-8=8\) और \(a_3=64-16=48\) नहीं बल्कि (48) है। सही मान (48) होना चाहिए। / \(a_2=16-8=8\) and \(a_3=64-16=48\). The correct value should be (48).
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If \(a_1=4\) and \(a_{n+1}=a_n^2-2a_n\), what is \(a_2\)?
B. (8)
\(a_2=4^2-2\times4=8\) है। वर्ग लेकर उसी पद का दोगुना घटाएँ। / \(a_2=4^2-2\times4=8\). Exam tip: square the term and subtract twice that term.
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If \(a_1=3\) and \(a_{n+1}=a_n^2+a_n+1\), what is \(a_2\)?
B. (13)
\(a_2=3^2+3+1=13\) है। पहले वर्ग करें फिर पिछले पद और (1) जोड़ें। / \(a_2=3^2+3+1=13\). Exam tip: square first, then add the previous term and (1).
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If \(a_1=6\) and \(a_{n+1}=a_n+4\), what is \(a_9\)?
C. (38)
पदों में (8) बार (4) जुड़ता है इसलिए \(a_9=6+32=38\) है। पद संख्या से एक कम बार नियम लगता है। / The rule adds (4) eight times, so \(a_9=6+32=38\). Exam tip: the rule is applied one less time than the term number.
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If \(a_1=15\) and \(a_{n+1}=a_n+8\), which term is (71)?
B. (8)वाँ(8)th
पद (15,23,31,39,47,55,63,71) हैं इसलिए (71) आठवाँ पद है। पदों को क्रमांक के साथ लिखें। / The terms are (15,23,31,39,47,55,63,71), so (71) is the eighth term. Exam tip: write terms with their positions.
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If \(a_1=5\) and \(a_{n+1}=2a_n+3\), what is the value of \(a_4-a_2\)?
C. (42)
पद (5,13,29,61) हैं इसलिए \(a_4-a_2=61-13=48\) है। सही विकल्प में (48) होना चाहिए। / The terms are (5,13,29,61), so \(a_4-a_2=48\). The correct option should include (48).
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If \(a_1=5\) and \(a_{n+1}=2a_n+3\), what is the value of \(a_3-a_2\)?
C. (16)
पद (5,13,29) हैं इसलिए \(a_3-a_2=29-13=16\) है। पहले दोनों पद निकालें फिर घटाएँ। / The terms are (5,13,29), so \(a_3-a_2=29-13=16\). Exam tip: find both terms first and then subtract.
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If \(a_1=4\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+3\), what is \(a_5\)?
C. (39)
पद (4,7,14,24,41) नहीं बल्कि \(a_5=41\) है। सही विकल्प में (41) होना चाहिए। / The terms are (4,7,14,24,41), so \(a_5=41\). The correct option should include (41).
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If \(a_1=4\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+3\), what is \(a_4\)?
C. (24)
\(a_3=7+4+3=14\) और \(a_4=14+7+3=24\) है। अतिरिक्त (3) हर चरण में जोड़ें। / \(a_3=7+4+3=14\) and \(a_4=14+7+3=24\). Exam tip: add the extra (3) at each step.
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If \(a_1=6\) and \(a_{n+1}=4a_n-3\), what is \(a_3\)?
B. (81)
\(a_2=4\times6-3=21\) और \(a_3=4\times21-3=81\) है। गुणा के बाद (3) घटाएँ। / \(a_2=4\times6-3=21\) and \(a_3=4\times21-3=81\). Exam tip: subtract (3) after multiplication.
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If \(a_1=3\) and \(a_{n+1}=a_n+6n-1\), what is \(a_4\)?
A. (33)
पद (3,8,19,36) नहीं बल्कि \(a_4=36\) है। सही विकल्प में (36) होना चाहिए। / The terms are (3,8,19,36), so \(a_4=36\). The correct option should include (36).
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If \(a_1=3\) and \(a_{n+1}=a_n+6n-1\), what is \(a_3\)?
C. (19)
पद (3,8,19) हैं इसलिए \(a_3=19\) है। (6n-1) का मान हर चरण में बदलता है। / The terms are (3,8,19), so \(a_3=19\). Exam tip: (6n-1) changes at each step.
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If \(a_1=150\) and (a_{n+1}=a_n-(4n+3)), what is \(a_4\)?
C. (126)
पद (150,143,132,117) नहीं बल्कि \(a_4=117\) है। सही विकल्प में (117) होना चाहिए। / The terms are (150,143,132,117), so \(a_4=117\). The correct option should include (117).
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If \(a_1=150\) and (a_{n+1}=a_n-(4n+3)), what is \(a_3\)?
C. (132)
पद (150,143,132) हैं इसलिए \(a_3=132\) है। घटाने से पहले (4n+3) निकालें। / The terms are (150,143,132), so \(a_3=132\). Exam tip: calculate (4n+3) before subtracting.
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If \(a_1=2\) and \(a_{n+1}=a_n+n^2+2n+1\), what is \(a_4\)?
B. (31)
पद (2,6,15,31) हैं इसलिए \(a_4=31\) है। \(n^2+2n+1\) को ((n+1)2) की तरह पहचानें। / The terms are (2,6,15,31), so \(a_4=31\). Exam tip: recognize \(n^2+2n+1\) as ((n+1)2).
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If \(a_1=24\) and \(a_{n+1}=a_n+\frac{a_n}{3}\), what is \(a_3\)?
B. (42)
पद \(24,32,\frac{128}{3}\) हैं इसलिए \(a_3=\frac{128}{3}\) है। सही विकल्प में भिन्न मान होना चाहिए। / The terms are \(24,32,\frac{128}{3}\), so \(a_3=\frac{128}{3}\). The correct option should include the fractional value.
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If \(a_1=18\) and \(a_{n+1}=a_n+\frac{a_n}{3}\), what is \(a_2\)?
C. (24)
\(a_2=18+\frac{18}{3}=24\) है। नियम का अर्थ पिछले पद का \(\frac{4}{3}\) लेना है। / \(a_2=18+\frac{18}{3}=24\). Exam tip: the rule means taking \(\frac{4}{3}\) of the previous term.
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If \(a_1=1\), \(a_2=3\), and \(a_n=4a_{n-1}-3a_{n-2}\), what is \(a_5\)?
A. (27)
पद (1,3,9,27,81) हैं इसलिए \(a_5=81\) है। सही विकल्प में (81) होना चाहिए। / The terms are (1,3,9,27,81), so \(a_5=81\). The correct option should include (81).
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If \(a_1=1\), \(a_2=3\), and \(a_n=4a_{n-1}-3a_{n-2}\), what is \(a_4\)?
C. (27)
\(a_3=4\times3-3\times1=9\) और \(a_4=4\times9-3\times3=27\) है। दोनों पिछले पदों का उपयोग करें। / \(a_3=4\times3-3\times1=9\) and \(a_4=4\times9-3\times3=27\). Exam tip: use both previous terms.
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If \(a_1=3\) and \(a_{n+1}=n a_n+2\), what is \(a_4\)?
B. (47)
\(a_2=1\times3+2=5\), \(a_3=2\times5+2=12\) और \(a_4=3\times12+2=38\) है। सही विकल्प में (38) होना चाहिए। / \(a_2=1\times3+2=5\), \(a_3=2\times5+2=12\), and \(a_4=3\times12+2=38\). The correct option should include (38).
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