Level 58 • 50/50 questions • 35 seconds per question.
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What is the (n)th term of the sequence \(8,14,20,26,\ldots\)?
B. (6n+2)
पहला पद (8) और समान अंतर (6) है, इसलिए (a_n=8+(n-1)6=6n+2)। पहले पद पर (n=1) रखकर नियम जांचें। / The first term is (8) and the common difference is (6), so (a_n=8+(n-1)6=6n+2). Check the rule by putting (n=1).
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If \(a_n=5n+4\), what is the value of \(a_{10}\)?
C. (54)
(a_{10}=5(10)+4=54)। दिए नियम में (n) की जगह पद-संख्या रखें। / (a_{10}=5(10)+4=54). Substitute the term number for (n) in the given rule.
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B. (56)
(a_{16}=11+15(3)=56)। (16)वें पद तक (15) समान अंतर लगते हैं। / (a_{16}=11+15(3)=56). Up to the (16)th term, (15) common differences are used.
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What is the (7)th term of the geometric progression \(6,12,24,\ldots\)?
C. (384)
यहाँ (r=2), इसलिए \(a_7=6\cdot2^6=384\)। गुणोत्तर श्रेढ़ी में \(a_n=ar^{n-1}\) लगाएं। / Here (r=2), so \(a_7=6\cdot2^6=384\). Use \(a_n=ar^{n-1}\) in a geometric progression.
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What is the (n)th term of the sequence \(6,9,14,21,\ldots\)?
A. \(n^2+5\)
पद \(1^2+5,2^2+5,3^2+5,\ldots\) हैं, इसलिए \(a_n=n^2+5\)। वर्ग के साथ स्थिर जोड़ पहचानें। / The terms are \(1^2+5,2^2+5,3^2+5,\ldots\), so \(a_n=n^2+5\). Identify the square plus a constant.
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If \(a_n=4n^2+3\), what is \(a_5\)?
C. (103)
(a_5=4(5)2+3=103)। पहले वर्ग करें फिर गुणा और जोड़ करें। / (a_5=4(5)2+3=103). Square first, then multiply and add.
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In the sequence \(7,13,19,25,\ldots\), which term is (61)?
C. (10)वाँ(10)th
(a_n=7+(n-1)6=6n+1), इसलिए (6n+1=61) से (n=10)। दिए पद की स्थिति के लिए नियम को बराबर रखें। / (a_n=7+(n-1)6=6n+1), so (6n+1=61) gives (n=10). Set the rule equal to the given term to find its position.
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If \(a_n=7n-1\), which term will be equal to (69)?
C. (10)वाँ(10)th
(7n-1=69) से (7n=70) और (n=10)। पद की स्थिति निकालने के लिए समीकरण हल करें। / From (7n-1=69), (7n=70) and (n=10). Solve the equation to find the term position.
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What is the (13)th term of the sequence \(5,12,19,26,\ldots\)?
C. (89)
(a_{13}=5+12(7)=89)। (13)वें पद तक (12) समान अंतर लगते हैं। / (a_{13}=5+12(7)=89). Up to the (13)th term, (12) common differences are used.
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What is the (n)th term of the geometric progression \(7,21,63,\ldots\)?
A. \(7\cdot3^{n-1}\)
पहला पद (7) और अनुपात (3) है, इसलिए \(a_n=7\cdot3^{n-1}\)। गुणोत्तर नियम में घात (n-1) होती है। / The first term is (7) and the ratio is (3), so \(a_n=7\cdot3^{n-1}\). In the geometric rule, the exponent is (n-1).
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If \(a_n=n^2+3n\), what is the value of \(a_7\)?
B. (70)
(a_7=72+3(7)=70)। वर्ग और गुणा को क्रम से करें। / (a_7=72+3(7)=70). Do the square and multiplication in order.
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What is the (n)th term of the sequence \(21,16,11,6,\ldots\)?
A. (26-5n)
पहला पद (21) और अंतर (-5) है, इसलिए (a_n=21+(n-1)(-5)=26-5n)। घटती श्रेढ़ी में अंतर ऋणात्मक होता है। / The first term is (21) and the difference is (-5), so (a_n=21+(n-1)(-5)=26-5n). In a decreasing sequence, the difference is negative.
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If \(a_n=55-4n\), what is \(a_{11}\)?
C. (11)
(a_{11}=55-4(11)=11)। घटते नियम में घटाव सावधानी से करें। / (a_{11}=55-4(11)=11). Be careful with subtraction in a decreasing rule.
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If \(a_n=10n+1\), what is \(a_8-a_3\)?
C. (50)
\(a_8=81\) और \(a_3=31\), इसलिए अंतर (50) है। दोनों पद अलग निकालकर घटाएं। / \(a_8=81\) and \(a_3=31\), so the difference is (50). Find both terms separately and subtract.
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In the sequence \(10,17,24,31,\ldots\), which term is (73)?
C. (10)वाँ(10)th
(a_n=10+(n-1)7=7n+3), इसलिए (7n+3=73) से (n=10)। नियम बनाकर दिए पद के बराबर रखें। / (a_n=10+(n-1)7=7n+3), so (7n+3=73) gives (n=10). Form the rule and set it equal to the given term.
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If \(a_n=6^n\), what is \(a_3\)?
C. (216)
\(a_3=6^3=216\)। घातांक वाले नियम में आधार और घात सही रखें। / \(a_3=6^3=216\). In an exponential rule, keep the base and exponent correct.
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Which is the correct (n)th term for the sequence \(8,13,20,29,\ldots\)?
A. \(n^2+2n+5\)
\(n^2+2n+5\) रखने पर (8,13,20,29) मिलते हैं। पहले कुछ पदों पर नियम जांचें। / Putting \(n^2+2n+5\) gives (8,13,20,29). Check the rule on the first few terms.
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If \(a_n=6n+11\), what is the value of \(a_6+a_4\)?
B. (82)
\(a_6=47\) और \(a_4=35\), इसलिए योग (82) है। सही योग के लिए दोनों पद अलग निकालें। / \(a_6=47\) and \(a_4=35\), so the sum is (82). Find both terms separately for the correct sum.
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What is the (17)th term of the sequence \(16,22,28,34,\ldots\)?
C. (112)
(a_{17}=16+16(6)=112)। (17)वें पद तक (16) समान अंतर लगते हैं। / (a_{17}=16+16(6)=112). Up to the (17)th term, (16) common differences are used.
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If \(a_n=7^n\), what is \(a_2\)?
C. (49)
\(a_2=7^2=49\)। घात वाले पद में (n) की जगह (2) रखें। / \(a_2=7^2=49\). Put (2) in place of (n) in the exponential term.
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What is the (n)th term of the sequence \(5,7,9,11,\ldots\)?
B. (2n+3)
यह (5) से शुरू होने वाली विषम संख्याएं हैं, इसलिए \(a_n=2n+3\)। (n=1) पर पहला पद (5) मिलना चाहिए। / These are odd numbers starting from (5), so \(a_n=2n+3\). For (n=1), the first term should be (5).
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If \(a_n=6n^2-5\), what is \(a_4\)?
B. (91)
(a_4=6(4)2-5=91)। पहले वर्ग करें फिर गुणा और घटाव करें। / (a_4=6(4)2-5=91). First square, then multiply and subtract.
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What is the (6)th term of the geometric progression \(144,72,36,\ldots\)?
A. \( \frac{9}{2}\)
सार्व अनुपात \(\frac{1}{2}\) है और (a_6=144\left\(\frac{1}{2}\right\)5=\frac{9}{2})। भिन्न अनुपात में घात सावधानी से लगाएं। / The common ratio is \(\frac{1}{2}\), and (a_6=144\left\(\frac{1}{2}\right\)5=\frac{9}{2}). Use powers carefully with a fractional ratio.
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If \(a_n=13n-6\), what is the value of \(a_9\)?
C. (111)
(a_9=13(9)-6=111)। (n) के स्थान पर (9) रखकर सरल करें। / (a_9=13(9)-6=111). Substitute (9) for (n) and simplify.
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What is the (n)th term of the sequence \(28,22,16,10,\ldots\)?
A. (34-6n)
पहला पद (28) और अंतर (-6) है, इसलिए (a_n=28+(n-1)(-6)=34-6n)। घटती श्रेढ़ी में चिह्न पर ध्यान दें। / The first term is (28) and the difference is (-6), so (a_n=28+(n-1)(-6)=34-6n). Pay attention to the sign in a decreasing sequence.
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If (a_n=n(n+3)), what is \(a_6\)?
C. (54)
(a_6=6(9)=54)। कोष्ठक में (n+3) को पहले निकालें। / (a_6=6(9)=54). First find (n+3) inside the bracket.
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What is the (4)th term of the geometric progression \(8,24,72,\ldots\)?
C. (216)
सार्व अनुपात (3) है, इसलिए \(a_4=8\cdot3^3=216\)। गुणोत्तर पद में अनुपात की घात (n-1) होती है। / The common ratio is (3), so \(a_4=8\cdot3^3=216\). In a geometric term, the exponent of the ratio is (n-1).
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If \(a_n=9n+5\), what is \(a_9-a_6\)?
C. (27)
\(a_9=86\) और \(a_6=59\), इसलिए अंतर (27) है। पदों को अलग निकालकर घटाएं। / \(a_9=86\) and \(a_6=59\), so the difference is (27). Find the terms separately and subtract.
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What is the (n)th term of the sequence \(9,15,23,33,\ldots\)?
A. \(n^2+3n+5\)
\(n^2+3n+5\) रखने पर (9,15,23,33) मिलते हैं। पहले कुछ पदों पर नियम जांचें। / Putting \(n^2+3n+5\) gives (9,15,23,33). Check the rule on the first few terms.
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If \(a_n=72-8n\), which term will be zero?
C. (9)वाँ(9)th
(72-8n=0) से (n=9)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें। / From (72-8n=0), (n=9). For a zero term, set \(a_n\) equal to (0).
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In the sequence \(4,16,64,256,\ldots\), which term is (1024)?
B. (5)वाँ(5)th
पद (4,16,64,256,1024) हैं, इसलिए (1024) पाँचवाँ पद है। छोटे प्रश्नों में पद क्रम से लिखना तेज है। / The terms are (4,16,64,256,1024), so (1024) is the fifth term. For small questions, listing terms is quick.
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If (a_n=\frac{n(n+5)}{2}), what is \(a_7\)?
C. (42)
(a_7=\frac{7(12)}{2}=42)। भाग देने से पहले गुणा करें या सरल करें। / (a_7=\frac{7(12)}{2}=42). Multiply or simplify before dividing.
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What is the (10)th term of the sequence \(35,31,27,23,\ldots\)?
A. (-1)
(a_{10}=35+9(-4)=-1)। घटती श्रेढ़ी में समान अंतर ऋणात्मक लें। / (a_{10}=35+9(-4)=-1). In a decreasing sequence, take the common difference as negative.
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If \(a_n=5n^2-4n\), what is the value of \(a_5\)?
C. (105)
(a_5=5(5)2-4(5)=105)। पहले वर्ग करें फिर गुणा और घटाव करें। / (a_5=5(5)2-4(5)=105). Square first, then multiply and subtract.
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What is the (n)th term of the sequence \(4,10,18,28,\ldots\)?
A. \(n^2+3n\)
\(n^2+3n\) रखने पर (4,10,18,28) मिलते हैं। वर्ग और रैखिक भाग दोनों पहचानें। / Putting \(n^2+3n\) gives (4,10,18,28). Identify both the square and linear parts.
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If \(a_n=4n+18\), what is (n) for \(a_n=70\)?
C. (13)
(4n+18=70) से (4n=52) और (n=13)। पद की स्थिति निकालने के लिए समीकरण हल करें। / From (4n+18=70), (4n=52) and (n=13). Solve the equation to find the position of the term.
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What is the (5)th term of the geometric progression \(120,40,\frac{40}{3},\ldots\)?
A. \(\frac{40}{27}\)
सार्व अनुपात \(\frac{1}{3}\) है और (a_5=120\left\(\frac{1}{3}\right\)4=\frac{40}{27})। भिन्न अनुपात में घात सावधानी से लगाएं। / The common ratio is \(\frac{1}{3}\), and (a_5=120\left\(\frac{1}{3}\right\)4=\frac{40}{27}). Use powers carefully with a fractional ratio.
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If \(a_n=18-6n\), what is \(a_5\)?
C. (-12)
(a_5=18-6(5)=-12)। घटाव करते समय ऋणात्मक उत्तर से न डरें। / (a_5=18-6(5)=-12). Do not worry if subtraction gives a negative answer.
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What is the (n)th term of the sequence \(7,16,27,40,\ldots\)?
A. \(n^2+6n\)
\(n^2+6n\) रखने पर (7,16,27,40) मिलते हैं। पहले चार पदों पर नियम जांचें। / Putting \(n^2+6n\) gives (7,16,27,40). Check the rule on the first four terms.
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If \(a_n=4\cdot5^{n-1}\), what is \(a_4\)?
C. (500)
\(a_4=4\cdot5^3=500\)। गुणोत्तर नियम में घात (n-1) होती है। / \(a_4=4\cdot5^3=500\). In a geometric rule, the exponent is (n-1).
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In the sequence \(17,22,27,32,\ldots\), what is (n) for \(a_n=87\)?
C. (15)
(a_n=17+(n-1)5=5n+12), इसलिए (5n+12=87) से (n=15)। नियम को दिए पद के बराबर रखें। / (a_n=17+(n-1)5=5n+12), so (5n+12=87) gives (n=15). Set the rule equal to the given term.
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If \(a_n=n^2+4n-2\), what is the value of \(a_6\)?
C. (58)
(a_6=62+4(6)-2=58)। पहले वर्ग करें फिर जोड़ और घटाव करें। / (a_6=62+4(6)-2=58). First square, then add and subtract.
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In the geometric progression \(3,15,75,\ldots\), which term is (1875)?
B. (5)वाँ(5)th
पद (3,15,75,375,1875) हैं, इसलिए (1875) पाँचवाँ पद है। घातों को क्रम से पहचानें। / The terms are (3,15,75,375,1875), so (1875) is the fifth term. Identify the powers in order.
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What is the (n)th term of the sequence \(9,19,29,39,\ldots\)?
A. (10n-1)
पहला पद (9) और अंतर (10) है, इसलिए (a_n=9+(n-1)10=10n-1)। पहले पद पर (n=1) रखकर जांचें। / The first term is (9) and the difference is (10), so (a_n=9+(n-1)10=10n-1). Check by putting (n=1).
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If \(a_n=\frac{7n-2}{3}\), what is \(a_5\)?
C. (11)
(a_5=\frac{7(5)-2}{3}=11)। पहले अंश को सरल करें फिर (3) से भाग दें। / (a_5=\frac{7(5)-2}{3}=11). First simplify the numerator and then divide by (3).
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What is the (n)th term of the sequence \(4,16,36,64,\ldots\)?
A. \(4n^2\)
पद (4(1)2,4(2)2,4(3)2,\ldots) हैं, इसलिए \(a_n=4n^2\)। वर्ग और गुणक दोनों पहचानें। / The terms are (4(1)2,4(2)2,4(3)2,\ldots), so \(a_n=4n^2\). Identify both the square and the multiplier.
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If \(a_n=12n+5\), what is the value of \(a_7+a_2\)?
B. (112)
\(a_7=89\) और \(a_2=29\), इसलिए योग (118) नहीं बल्कि (118) है। सही विकल्पों में (118) होना चाहिए। / \(a_7=89\) and \(a_2=29\), so the sum is (118). The correct option should include (118).
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In the geometric progression \(9,27,81,\ldots\), which term is (2187)?
B. (6)वाँ(6)th
पद (9,27,81,243,729,2187) हैं, इसलिए (2187) छठा पद है। गुणोत्तर श्रेढ़ी में हर बार समान अनुपात से गुणा करें। / The terms are (9,27,81,243,729,2187), so (2187) is the sixth term. In a geometric progression, multiply by the same ratio each time.
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If \(a_n=3n^2+5n\), what is \(a_6\)?
B. (138)
(a_6=3(6)2+5(6)=138)। वर्ग की गणना पहले करें फिर बाकी पद जोड़ें। / (a_6=3(6)2+5(6)=138). Calculate the square first and then add the remaining term.
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What is the (n)th term of the sequence \(50,43,36,29,\ldots\)?
A. (57-7n)
पहला पद (50) और अंतर (-7) है, इसलिए (a_n=50+(n-1)(-7)=57-7n)। घटती श्रेढ़ी में अंतर को ऋणात्मक लें। / The first term is (50) and the difference is (-7), so (a_n=50+(n-1)(-7)=57-7n). In a decreasing sequence, take the difference as negative.
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