Level 48 • 50/50 questions • 40 seconds per question.
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If \(a_1=4\) and \(a_{n+1}=a_n+2\), what is \(a_5\)?
B. (12)
पद (4,6,8,10,12) हैं इसलिए \(a_5=12\) है। हर चरण में (2) जोड़ें। / The terms are (4,6,8,10,12), so \(a_5=12\). Exam tip: add (2) at each step.
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If \(a_1=18\) and \(a_{n+1}=a_n-3\), what is \(a_4\)?
D. (9)
पद (18,15,12,9) हैं इसलिए \(a_4=9\) है। घटाने वाले नियम में चिह्न सही रखें। / The terms are (18,15,12,9), so \(a_4=9\). Exam tip: keep the sign correct in subtraction rules.
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If \(a_1=5\) and \(a_{n+1}=2a_n\), what is the value of \(a_3\)?
A. (20)
पद (5,10,20) हैं इसलिए \(a_3=20\) है। हर बार पिछले पद को (2) से गुणा करें। / The terms are (5,10,20), so \(a_3=20\). Exam tip: multiply the previous term by (2) each time.
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If \(a_1=48\) and \(a_{n+1}=\frac{a_n}{2}\), what is \(a_5\)?
C. (3)
पद (48,24,12,6,3) हैं इसलिए \(a_5=3\) है। भाग वाले नियम में हर बार नया पद आधा करें। / The terms are (48,24,12,6,3), so \(a_5=3\). Exam tip: halve the newest term each time.
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If \(a_1=2\) and \(a_{n+1}=a_n+n\), what is \(a_4\)?
C. (8)
पद (2,3,5,8) हैं इसलिए \(a_4=8\) है। यहाँ (n) का मान हर चरण में बदलता है। / The terms are (2,3,5,8), so \(a_4=8\). Exam tip: the value of (n) changes at each step.
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If \(a_1=15\) and \(a_{n+1}=a_n-n\), what is \(a_5\)?
A. (7)
पद (15,14,12,9,5) नहीं बल्कि \(a_5=5\) होता है। दिए गए विकल्पों में सही मान नहीं है। / The terms are (15,14,12,9,5), so \(a_5=5\). None of the listed options is correct.
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If \(a_1=15\) and \(a_{n+1}=a_n-n\), what is \(a_4\)?
C. (9)
पद (15,14,12,9) हैं इसलिए \(a_4=9\) है। (n) को (1,2,3) के क्रम में घटाएँ। / The terms are (15,14,12,9), so \(a_4=9\). Exam tip: subtract (n) in the order (1,2,3).
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If \(a_1=3\) and \(a_{n+1}=a_n+2n\), what is \(a_5\)?
D. (23)
पद (3,5,9,15,23) हैं इसलिए \(a_5=23\) है। पहले (2n) निकालें फिर जोड़ें। / The terms are (3,5,9,15,23), so \(a_5=23\). Exam tip: find (2n) first and then add.
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If \(a_1=6\) and (a_{n+1}=a_n+(2n-1)), what is \(a_5\)?
C. (22)
पद (6,7,10,15,22) हैं इसलिए \(a_5=22\) है। (2n-1) से (1,3,5,7) जुड़ते हैं। / The terms are (6,7,10,15,22), so \(a_5=22\). Exam tip: (2n-1) adds (1,3,5,7).
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If \(a_1=4\) and \(a_{n+1}=3a_n\), what is \(a_3\)?
B. (36)
पद (4,12,36) हैं इसलिए \(a_3=36\) है। पिछले पद को (3) से गुणा करें। / The terms are (4,12,36), so \(a_3=36\). Exam tip: multiply the previous term by (3).
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If \(a_1=2\) and \(a_{n+1}=2a_n+1\), what is \(a_4\)?
D. (23)
पद (2,5,11,23) हैं इसलिए \(a_4=23\) है। पहले दोगुना करें फिर (1) जोड़ें। / The terms are (2,5,11,23), so \(a_4=23\). Exam tip: double first and then add (1).
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If \(a_1=6\) and \(a_{n+1}=2a_n-2\), what is the value of \(a_3\)?
C. (18)
पद (6,10,18) हैं इसलिए \(a_3=18\) है। नियम में घटाव गुणा के बाद करें। / The terms are (6,10,18), so \(a_3=18\). Exam tip: subtract after multiplication.
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If \(a_1=1\) and \(a_{n+1}=a_n+6\), what is \(a_6\)?
D. (31)
पद (1,7,13,19,25,31) हैं इसलिए \(a_6=31\) है। समान जोड़ में क्रमांक सावधानी से गिनें। / The terms are (1,7,13,19,25,31), so \(a_6=31\). Exam tip: count positions carefully in constant addition.
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If \(a_1=45\) and \(a_{n+1}=a_n-5\), what is \(a_6\)?
B. (20)
पद (45,40,35,30,25,20) हैं इसलिए \(a_6=20\) है। हर बार (5) घटाएँ। / The terms are (45,40,35,30,25,20), so \(a_6=20\). Exam tip: subtract (5) at each step.
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If \(a_1=1\), \(a_2=3\), and \(a_n=a_{n-1}+a_{n-2}\), what is \(a_6\)?
C. (18)
पद (1,3,4,7,11,18) हैं इसलिए \(a_6=18\) है। पिछले दो पदों को जोड़कर अगला पद बनता है। / The terms are (1,3,4,7,11,18), so \(a_6=18\). Exam tip: add the previous two terms to get the next one.
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If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}\), what is \(a_5\)?
D. (22)
पद (2,6,8,14,22) हैं इसलिए \(a_5=22\) है। दो पिछले पदों को सही क्रम में जोड़ें। / The terms are (2,6,8,14,22), so \(a_5=22\). Exam tip: add the previous two terms in the correct order.
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If \(a_1=27\) and \(a_{n+1}=\frac{a_n}{3}\), what is \(a_4\)?
A. (1)
पद (27,9,3,1) हैं इसलिए \(a_4=1\) है। हर चरण में (3) से भाग दें। / The terms are (27,9,3,1), so \(a_4=1\). Exam tip: divide by (3) at every step.
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If \(a_1=8\) and \(a_{n+1}=a_n+3\), which term is (20)?
C. (5)वाँ(5)th
पद (8,11,14,17,20) हैं इसलिए (20) पाँचवाँ पद है। पदों को क्रमांक के साथ लिखें। / The terms are (8,11,14,17,20), so (20) is the fifth term. Exam tip: write terms with their positions.
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If \(a_1=6\) and \(a_{n+1}=a_n+6\), which term is (30)?
B. (5)वाँ(5)th
पद (6,12,18,24,30) हैं इसलिए (30) पाँचवाँ पद है। समान वृद्धि में क्रम से गिनें। / The terms are (6,12,18,24,30), so (30) is the fifth term. Exam tip: count step by step in constant growth.
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Which recursive rule is correct for the sequence \(7,11,15,19,\ldots\)?
A. \(a_1=7, a_{n+1}=a_n+4\)
पहला पद (7) है और हर बार (4) जुड़ता है। नियम में पहला पद और जोड़ दोनों सही होने चाहिए। / The first term is (7), and (4) is added each time. Exam tip: both the first term and addition must be correct.
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Which recursive rule is correct for the sequence \(25,20,15,10,\ldots\)?
C. \(a_1=25, a_{n+1}=a_n-5\)
पहला पद (25) है और हर बार (5) घटता है। घटते अनुक्रम में (-) चिह्न देखें। / The first term is (25), and (5) is subtracted each time. Exam tip: watch the (-) sign in decreasing sequences.
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What is the recursive rule for the sequence \(4,12,36,108,\ldots\)?
C. \(a_1=4, a_{n+1}=3a_n\)
पहला पद (4) है और हर पद पिछले का (3) गुना है। गुणा नियम पहचानने के लिए अनुपात देखें। / The first term is (4), and each term is (3) times the previous one. Exam tip: check the ratio to identify multiplication rules.
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Which recursive rule matches the sequence \(100,50,25,\ldots\)?
C. \(a_1=100, a_{n+1}=\frac{a_n}{2}\)
पहला पद (100) है और हर बार आधा किया गया है। पहला पद और क्रिया दोनों सही देखें। / The first term is (100), and each term is halved. Exam tip: check both the first term and the operation.
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If \(a_1=12\) and \(a_{n+1}=a_n+1\), what is \(a_5\)?
C. (16)
पद (12,13,14,15,16) हैं इसलिए \(a_5=16\) है। छोटे जोड़ में भी क्रमांक सावधानी से गिनें। / The terms are (12,13,14,15,16), so \(a_5=16\). Exam tip: count positions carefully even in small additions.
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If \(a_1=80\) and \(a_{n+1}=a_n-20\), what is \(a_4\)?
B. (20)
पद (80,60,40,20) हैं इसलिए \(a_4=20\) है। हर बार (20) घटाएँ। / The terms are (80,60,40,20), so \(a_4=20\). Exam tip: subtract (20) each time.
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If \(a_1=7\) and \(a_{n+1}=a_n+3\), what is the value of \(a_5-a_2\)?
B. (9)
पद (7,10,13,16,19) हैं इसलिए \(a_5-a_2=19-10=9\) है। पहले दोनों पद निकालें। / The terms are (7,10,13,16,19), so \(a_5-a_2=19-10=9\). Exam tip: find both terms first.
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If \(a_1=5\) and \(a_{n+1}=a_n+4\), what is \(a_3+a_4\)?
C. (26)
पद (5,9,13,17) हैं और \(a_3+a_4=13+17=30\) नहीं है इसलिए विकल्प सही नहीं हैं। / The terms are (5,9,13,17), and \(a_3+a_4=30\). None of the options is correct.
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If \(a_1=5\) and \(a_{n+1}=a_n+4\), what is \(a_2+a_4\)?
C. (26)
पद (5,9,13,17) हैं और \(a_2+a_4=9+17=26\) है। योग से पहले जरूरी पद निकालें। / The terms are (5,9,13,17), and \(a_2+a_4=9+17=26\). Exam tip: find the needed terms before adding.
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If \(a_1=3\) and \(a_{n+1}=a_n^2\), what is \(a_2\)?
B. (9)
\(a_2=3^2=9\) है। वर्ग वाले नियम में पिछले पद का वर्ग लें। / \(a_2=3^2=9\). Exam tip: square the previous term in square rules.
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If \(a_1=2\) and \(a_{n+1}=a_n^2+2\), what is \(a_2\)?
C. (6)
\(a_2=2^2+2=6\) है। पहले वर्ग करें फिर (2) जोड़ें। / \(a_2=2^2+2=6\). Exam tip: square first and then add (2).
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If \(a_1=120\) and \(a_{n+1}=a_n-25\), what is \(a_3\)?
B. (70)
पद (120,95,70) हैं इसलिए \(a_3=70\) है। बड़े घटाव में भी चरण न छोड़ें। / The terms are (120,95,70), so \(a_3=70\). Exam tip: do not skip steps even with large subtraction.
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If \(a_1=13\) and \(a_{n+1}=a_n+8\), what is \(a_4\)?
C. (37)
पद (13,21,29,37) हैं इसलिए \(a_4=37\) है। हर बार (8) जोड़ें। / The terms are (13,21,29,37), so \(a_4=37\). Exam tip: add (8) each time.
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If \(a_1=3\) and \(a_{n+1}=5a_n\), what is \(a_3\)?
D. (75)
पद (3,15,75) हैं इसलिए \(a_3=75\) है। पिछले पद को (5) से गुणा करें। / The terms are (3,15,75), so \(a_3=75\). Exam tip: multiply the previous term by (5).
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If \(a_1=4\) and \(a_{n+1}=3a_n+1\), what is \(a_2\)?
B. (13)
\(a_2=3\times4+1=13\) है। अगले पद के लिए सीधे \(a_1\) पर नियम लगाएँ। / \(a_2=3\times4+1=13\). Exam tip: apply the rule directly to \(a_1\) for the next term.
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If \(a_1=36\) and \(a_{n+1}=\frac{a_n}{2}+2\), what is \(a_2\)?
B. (20)
\(a_2=\frac{36}{2}+2=20\) है। पहले आधा करें फिर (2) जोड़ें। / \(a_2=\frac{36}{2}+2=20\). Exam tip: halve first and then add (2).
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If \(a_1=2\) and \(a_{n+1}=a_n+4n\), what is \(a_4\)?
D. (26)
पद (2,6,14,26) हैं इसलिए \(a_4=26\) है। (4n) का मान हर चरण में बदलता है। / The terms are (2,6,14,26), so \(a_4=26\). Exam tip: (4n) changes at every step.
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If \(a_1=30\) and (a_{n+1}=a_n-(n+2)), what is \(a_3\)?
B. (23)
पद (30,27,23) हैं इसलिए \(a_3=23\) है। प्रत्येक चरण में (n+2) सही निकालें। / The terms are (30,27,23), so \(a_3=23\). Exam tip: calculate (n+2) correctly at each step.
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If \(a_1=5\), \(a_2=8\), and \(a_n=a_{n-1}+3\), what is \(a_5\)?
B. (17)
पद (5,8,11,14,17) हैं इसलिए \(a_5=17\) है। \(a_n\) पिछले पद से (3) अधिक है। / The terms are (5,8,11,14,17), so \(a_5=17\). Exam tip: \(a_n\) is (3) more than the previous term.
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If \(a_1=2\), \(a_2=4\), and \(a_n=3a_{n-1}\), what is \(a_4\)?
C. (36)
\(a_3=12\) और \(a_4=36\) है। पिछले पद को हर बार (3) से गुणा करें। / \(a_3=12\) and \(a_4=36\). Exam tip: multiply the previous term by (3) each time.
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If \(a_1=5\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}\), what is \(a_6\)?
B. (36)
पद (5,7,12,19,31,50) नहीं बल्कि \(a_6=50\) है। दिए गए विकल्पों में सही मान नहीं है। / The terms are (5,7,12,19,31,50), so \(a_6=50\). None of the listed options is correct.
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If \(a_1=5\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}\), what is \(a_5\)?
C. (31)
पद (5,7,12,19,31) हैं इसलिए \(a_5=31\) है। पिछले दो पदों को जोड़कर नया पद बनता है। / The terms are (5,7,12,19,31), so \(a_5=31\). Exam tip: add the previous two terms to get the new term.
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According to the recursive rule in the sequence \(9,13,17,21,\ldots\), what is the next term?
C. (25)
हर बार (4) जोड़ा गया है इसलिए अगला पद (21+4=25) है। अंतर देखकर अगला पद निकालें। / (4) is added each time, so the next term is (21+4=25). Exam tip: use the difference to find the next term.
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According to the recursive rule in the sequence \(64,32,16,8,\ldots\), what will be the next term?
C. (4)
हर बार पद आधा हो रहा है इसलिए अगला पद (4) है। पिछले पद को (2) से भाग दें। / Each term is being halved, so the next term is (4). Exam tip: divide the previous term by (2).
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For the sequence \(8,16,24,32,\ldots\), \(a_1=8\). What is added in the recursive rule?
C. (8)
हर अगला पद पिछले से (8) अधिक है। इसलिए नियम \(a_{n+1}=a_n+8\) होगा। / Each next term is (8) more than the previous term. So the rule is \(a_{n+1}=a_n+8\).
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For the sequence \(42,36,30,24,\ldots\), what is subtracted in the recursive rule?
C. (6)
हर अगला पद पिछले से (6) कम है। इसलिए \(a_{n+1}=a_n-6\) होगा। / Each next term is (6) less than the previous term. So \(a_{n+1}=a_n-6\).
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In the sequence \(5,20,80,320,\ldots\), what is the multiplier in the recursive rule?
C. (4)
हर अगला पद पिछले पद का (4) गुना है। इसलिए गुणक (4) है। / Each next term is (4) times the previous term. Therefore the multiplier is (4).
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If \(a_1=14\) and \(a_{n+1}=a_n+7\), what is \(a_4\)?
B. (35)
पद (14,21,28,35) हैं इसलिए \(a_4=35\) है। तीन बार (7) जोड़ना है। / The terms are (14,21,28,35), so \(a_4=35\). Exam tip: add (7) three times.
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If \(a_1=6\) and \(a_{n+1}=a_n+10\), what is the value of \(a_3\)?
C. (26)
पद (6,16,26) हैं इसलिए \(a_3=26\) है। समान जोड़ को हर चरण में दोहराएँ। / The terms are (6,16,26), so \(a_3=26\). Exam tip: repeat the constant addition at every step.
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If \(a_1=96\) and \(a_{n+1}=\frac{a_n}{4}\), what is \(a_3\)?
B. (6)
पद (96,24,6) हैं इसलिए \(a_3=6\) है। हर बार पिछले पद को (4) से भाग दें। / The terms are (96,24,6), so \(a_3=6\). Exam tip: divide the previous term by (4) each time.
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If \(a_1=1\), \(a_2=5\), and \(a_n=a_{n-1}+a_{n-2}\), what is \(a_5\)?
C. (17)
पद (1,5,6,11,17) हैं इसलिए \(a_5=17\) है। पिछले दो पदों को सही क्रम में जोड़ें। / The terms are (1,5,6,11,17), so \(a_5=17\). Exam tip: add the previous two terms in the correct order.
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