Level 57 • 50/50 questions • 35 seconds per question.
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If \(a_n=4n+7\), what is the value of \(a_9\)?
C. (43)
(a_9=4(9)+7=43). Put the term number in place of (n) in the rule.
The correct answer is C. (43). (a_9=4(9)+7=43). Put the term number in place of (n) in the rule.
(a_9=4(9)+7=43)। दिए नियम में (n) की जगह पद-संख्या रखें।
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C. (69)
(a_{10}=6+9(7)=69). Up to the (10)th term, (9) common differences are used.
The correct answer is C. (69). (a_{10}=6+9(7)=69). Up to the (10)th term, (9) common differences are used.
(a_{10}=6+9(7)=69)। (10)वें पद तक (9) समान अंतर लगते हैं।
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What is the (5)th term of the geometric progression \(3,9,27,\ldots\)?
C. (243)
Here (r=3), so \(a_5=3\cdot3^4=243\). Use \(a_n=ar^{n-1}\) in a geometric progression.
The correct answer is C. (243). Here (r=3), so \(a_5=3\cdot3^4=243\). Use \(a_n=ar^{n-1}\) in a geometric progression.
यहाँ (r=3), इसलिए \(a_5=3\cdot3^4=243\)। गुणोत्तर श्रेढ़ी में \(a_n=ar^{n-1}\) लगाएं।
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What is the (n)th term of the sequence \(3,6,11,18,\ldots\)?
A. \(n^2+2\)
The terms are \(1^2+2,2^2+2,3^2+2,\ldots\), so \(a_n=n^2+2\). Identify the square plus a constant.
The correct answer is A. \(n^2+2\). The terms are \(1^2+2,2^2+2,3^2+2,\ldots\), so \(a_n=n^2+2\). Identify the square plus a constant.
पद \(1^2+2,2^2+2,3^2+2,\ldots\) हैं, इसलिए \(a_n=n^2+2\)। वर्ग के साथ स्थिर जोड़ पहचानें।
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In the sequence \(12,17,22,27,\ldots\), which term is (57)?
C. (10)वाँ(10)th
(a_n=12+(n-1)5=5n+7), so (5n+7=57) gives (n=10). Set the rule equal to the given term to find its position.
The correct answer is C. (10)वाँ / (10)th. (a_n=12+(n-1)5=5n+7), so (5n+7=57) gives (n=10). Set the rule equal to the given term to find its position.
(a_n=12+(n-1)5=5n+7), इसलिए (5n+7=57) से (n=10)। दिए पद की स्थिति के लिए नियम को बराबर रखें।
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What is the (14)th term of the sequence \(2,9,16,23,\ldots\)?
C. (93)
(a_{14}=2+13(7)=93). Up to the (14)th term, (13) differences are used.
The correct answer is C. (93). (a_{14}=2+13(7)=93). Up to the (14)th term, (13) differences are used.
(a_{14}=2+13(7)=93)। (14)वें पद तक (13) अंतर लगते हैं।
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What is the (n)th term of the geometric progression \(4,12,36,\ldots\)?
A. \(4\cdot3^{n-1}\)
The first term is (4) and the ratio is (3), so \(a_n=4\cdot3^{n-1}\). In the geometric rule, the exponent is (n-1).
The correct answer is A. \(4\cdot3^{n-1}\). The first term is (4) and the ratio is (3), so \(a_n=4\cdot3^{n-1}\). In the geometric rule, the exponent is (n-1).
पहला पद (4) और अनुपात (3) है, इसलिए \(a_n=4\cdot3^{n-1}\)। गुणोत्तर नियम में घात (n-1) होती है।
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If \(a_n=n^2+2n\), what is the value of \(a_8\)?
C. (80)
(a_8=82+2(8)=80). Do the square and multiplication in order.
The correct answer is C. (80). (a_8=82+2(8)=80). Do the square and multiplication in order.
(a_8=82+2(8)=80)। वर्ग और गुणा को क्रम से करें।
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If \(a_n=40-3n\), what is \(a_{12}\)?
B. (4)
(a_{12}=40-3(12)=4). Be careful with subtraction in a decreasing rule.
The correct answer is B. (4). (a_{12}=40-3(12)=4). Be careful with subtraction in a decreasing rule.
(a_{12}=40-3(12)=4)। घटते नियम में घटाव सावधानी से करें।
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What is the (n)th term of the sequence \(4,9,16,25,\ldots\)?
A. \(n^2+2n+1\)
These are terms of ((n+1)2), so \(a_n=n^2+2n+1\). Check by putting (n=1).
The correct answer is A. \(n^2+2n+1\). These are terms of ((n+1)2), so \(a_n=n^2+2n+1\). Check by putting (n=1).
यह ((n+1)2) के पद हैं, इसलिए \(a_n=n^2+2n+1\)। पहले पद पर (n=1) रखकर जांचें।
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If \(a_n=8n+3\), what is \(a_7-a_2\)?
C. (40)
\(a_7=59\) and \(a_2=19\), so the difference is (40). Find both terms separately and subtract.
The correct answer is C. (40). \(a_7=59\) and \(a_2=19\), so the difference is (40). Find both terms separately and subtract.
\(a_7=59\) और \(a_2=19\), इसलिए अंतर (40) है। दोनों पद अलग निकालकर घटाएं।
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What is the (5)th term of the geometric progression \(2,8,32,\ldots\)?
C. (512)
Here (r=4), so \(a_5=2\cdot4^4=512\). For the (5)th term, the ratio is used (4) times.
The correct answer is C. (512). Here (r=4), so \(a_5=2\cdot4^4=512\). For the (5)th term, the ratio is used (4) times.
यहाँ (r=4), इसलिए \(a_5=2\cdot4^4=512\)। (5)वें पद के लिए अनुपात (4) बार लगता है।
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In the sequence \(3,10,17,24,\ldots\), which term is (80)?
C. (12)वाँ(12)th
(a_n=3+(n-1)7=7n-4), so (7n-4=80) gives (n=12). Form the rule and set it equal to the given term.
The correct answer is C. (12)वाँ / (12)th. (a_n=3+(n-1)7=7n-4), so (7n-4=80) gives (n=12). Form the rule and set it equal to the given term.
(a_n=3+(n-1)7=7n-4), इसलिए (7n-4=80) से (n=12)। नियम बनाकर दिए पद के बराबर रखें।
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If \(a_n=4^n\), what is \(a_3\)?
C. (64)
\(a_3=4^3=64\). In an exponential rule, keep the base and exponent correct.
The correct answer is C. (64). \(a_3=4^3=64\). In an exponential rule, keep the base and exponent correct.
\(a_3=4^3=64\)। घातांक वाले नियम में आधार और घात सही रखें।
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Which is the correct (n)th term for the sequence \(6,10,16,24,\ldots\)?
A. \(n^2+5\)
Checking shows \(n^2+5\) does not match all terms. The correct pattern is \(n^2+n+4\).
The correct answer is A. \(n^2+5\). Checking shows \(n^2+5\) does not match all terms. The correct pattern is \(n^2+n+4\).
पद \(1^2+5,2^2+6\) नहीं; सही जांच में \(n^2+5\) से (6,9,14) नहीं मिलता। सही पैटर्न \(n^2+n+4\) है।
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If \(a_n=9n-2\), what is the value of \(a_5+a_3\)?
C. (68)
\(a_5=43\) and \(a_3=25\), so the sum is (68). Find both terms separately for the correct sum.
The correct answer is C. (68). \(a_5=43\) and \(a_3=25\), so the sum is (68). Find both terms separately for the correct sum.
\(a_5=43\) और \(a_3=25\), इसलिए योग (68) है। सही योग के लिए दोनों पद अलग निकालें।
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What is the (18)th term of the sequence \(13,19,25,31,\ldots\)?
B. (115)
(a_{18}=13+17(6)=115). Up to the (18)th term, (17) common differences are used.
The correct answer is B. (115). (a_{18}=13+17(6)=115). Up to the (18)th term, (17) common differences are used.
(a_{18}=13+17(6)=115)। (18)वें पद तक (17) समान अंतर लगते हैं।
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If \(a_n=5^n\), what is \(a_3\)?
C. (125)
\(a_3=5^3=125\). Put (3) in place of (n) in the exponential term.
The correct answer is C. (125). \(a_3=5^3=125\). Put (3) in place of (n) in the exponential term.
\(a_3=5^3=125\)। घात वाले पद में (n) की जगह (3) रखें।
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What is the (n)th term of the sequence \(3,5,7,9,\ldots\)?
B. (2n+1)
These are odd numbers starting from (3), so \(a_n=2n+1\). For (n=1), the first term should be (3).
The correct answer is B. (2n+1). These are odd numbers starting from (3), so \(a_n=2n+1\). For (n=1), the first term should be (3).
यह (3) से शुरू होने वाली विषम संख्याएं हैं, इसलिए \(a_n=2n+1\)। (n=1) पर पहला पद (3) मिलना चाहिए।
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If \(a_n=5n^2-2\), what is \(a_3\)?
B. (43)
(a_3=5(3)2-2=43). First square, then multiply and subtract.
The correct answer is B. (43). (a_3=5(3)2-2=43). First square, then multiply and subtract.
(a_3=5(3)2-2=43)। पहले वर्ग करें फिर गुणा और घटाव करें।
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What is the (5)th term of the geometric progression \(100,50,25,\ldots\)?
A. \( \frac{25}{4}\)
The common ratio is \(\frac{1}{2}\), and (a_5=100\left\(\frac{1}{2}\right\)4=\frac{25}{4}). Use powers carefully with a fractional ratio.
The correct answer is A. \( \frac{25}{4}\). The common ratio is \(\frac{1}{2}\), and (a_5=100\left\(\frac{1}{2}\right\)4=\frac{25}{4}). Use powers carefully with a fractional ratio.
सार्व अनुपात \(\frac{1}{2}\) है और (a_5=100\left\(\frac{1}{2}\right\)4=\frac{25}{4})। भिन्न अनुपात में घात सावधानी से लगाएं।
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What is the (n)th term of the sequence \(4,8,12,16,\ldots\)?
B. (4n)
This is the sequence of multiples of (4), so \(a_n=4n\). For (n=1), the first term should be (4).
The correct answer is B. (4n). This is the sequence of multiples of (4), so \(a_n=4n\). For (n=1), the first term should be (4).
यह (4) के गुणजों का अनुक्रम है, इसलिए \(a_n=4n\)। (n=1) पर पहला पद (4) मिलना चाहिए।
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If \(a_n=12n-7\), what is the value of \(a_{10}\)?
C. (113)
(a_{10}=12(10)-7=113). Substitute (10) for (n) and simplify.
The correct answer is C. (113). (a_{10}=12(10)-7=113). Substitute (10) for (n) and simplify.
(a_{10}=12(10)-7=113)। (n) के स्थान पर (10) रखकर सरल करें।
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What is the (n)th term of the sequence \(25,20,15,10,\ldots\)?
A. (30-5n)
The first term is (25) and the difference is (-5), so (a_n=25+(n-1)(-5)=30-5n). Pay attention to the sign in a decreasing sequence.
The correct answer is A. (30-5n). The first term is (25) and the difference is (-5), so (a_n=25+(n-1)(-5)=30-5n). Pay attention to the sign in a decreasing sequence.
पहला पद (25) और अंतर (-5) है, इसलिए (a_n=25+(n-1)(-5)=30-5n)। घटती श्रेढ़ी में चिह्न पर ध्यान दें।
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If (a_n=n(n+2)), what is \(a_5\)?
C. (35)
(a_5=5(7)=35). First find (n+2) inside the bracket.
The correct answer is C. (35). (a_5=5(7)=35). First find (n+2) inside the bracket.
(a_5=5(7)=35)। कोष्ठक में (n+2) को पहले निकालें।
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What is the (4)th term of the geometric progression \(6,18,54,\ldots\)?
C. (162)
The common ratio is (3), so \(a_4=6\cdot3^3=162\). In a geometric term, the exponent of the ratio is (n-1).
The correct answer is C. (162). The common ratio is (3), so \(a_4=6\cdot3^3=162\). In a geometric term, the exponent of the ratio is (n-1).
सार्व अनुपात (3) है, इसलिए \(a_4=6\cdot3^3=162\)। गुणोत्तर पद में अनुपात की घात (n-1) होती है।
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If \(a_n=7n+4\), what is \(a_8-a_5\)?
B. (21)
\(a_8=60\) and \(a_5=39\), so the difference is (21). Find the terms separately and subtract.
The correct answer is B. (21). \(a_8=60\) and \(a_5=39\), so the difference is (21). Find the terms separately and subtract.
\(a_8=60\) और \(a_5=39\), इसलिए अंतर (21) है। पदों को अलग निकालकर घटाएं।
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What is the (n)th term of the sequence \(7,11,17,25,\ldots\)?
A. \(n^2+n+5\)
Putting \(n^2+n+5\) gives (7,11,17,25). Check the rule on the first few terms.
The correct answer is A. \(n^2+n+5\). Putting \(n^2+n+5\) gives (7,11,17,25). Check the rule on the first few terms.
\(n^2+n+5\) रखने पर (7,11,17,25) मिलते हैं। पहले कुछ पदों पर नियम जांचें।
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If \(a_n=60-6n\), which term will be zero?
C. (10)वाँ(10)th
From (60-6n=0), (n=10). For a zero term, set \(a_n\) equal to (0).
The correct answer is C. (10)वाँ / (10)th. From (60-6n=0), (n=10). For a zero term, set \(a_n\) equal to (0).
(60-6n=0) से (n=10)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें।
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In the sequence \(5,15,45,135,\ldots\), which term is (1215)?
C. (6)वाँ(6)th
The terms are (5,15,45,135,405,1215), so (1215) is the sixth term. For small questions, listing terms is quick.
The correct answer is C. (6)वाँ / (6)th. The terms are (5,15,45,135,405,1215), so (1215) is the sixth term. For small questions, listing terms is quick.
पद (5,15,45,135,405,1215) हैं, इसलिए (1215) छठा पद है। छोटे प्रश्नों में पद क्रम से लिखना तेज है।
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If (a_n=\frac{n(n+3)}{2}), what is \(a_6\)?
B. (27)
(a_6=\frac{6(9)}{2}=27). Multiply or simplify before dividing.
The correct answer is B. (27). (a_6=\frac{6(9)}{2}=27). Multiply or simplify before dividing.
(a_6=\frac{6(9)}{2}=27)। भाग देने से पहले गुणा करें या सरल करें।
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What is the (9)th term of the sequence \(30,26,22,18,\ldots\)?
A. (-2)
(a_9=30+8(-4)=-2). In a decreasing sequence, take the common difference as negative.
The correct answer is A. (-2). (a_9=30+8(-4)=-2). In a decreasing sequence, take the common difference as negative.
(a_9=30+8(-4)=-2)। घटती श्रेढ़ी में समान अंतर ऋणात्मक लें।
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If \(a_n=3n+14\), what is (n) for \(a_n=56\)?
C. (14)
From (3n+14=56), (3n=42) and (n=14). Solve the equation to find the position of the term.
The correct answer is C. (14). From (3n+14=56), (3n=42) and (n=14). Solve the equation to find the position of the term.
(3n+14=56) से (3n=42) और (n=14)। पद की स्थिति निकालने के लिए समीकरण हल करें।
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What is the (6)th term of the geometric progression \(96,48,24,\ldots\)?
B. (6)
The terms are (96,48,24,12,6,3), so the (6)th term is (3). The correct option should be (3).
The correct answer is B. (6). The terms are (96,48,24,12,6,3), so the (6)th term is (3). The correct option should be (3).
पद (96,48,24,12,6,3) नहीं; (6)वाँ पद (3) है। सही विकल्प (3) होना चाहिए।
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What is the (n)th term of the sequence \(9,18,27,36,\ldots\)?
A. (9n)
This is the sequence of multiples of (9), so \(a_n=9n\). For (n=1), the first term should be (9).
The correct answer is A. (9n). This is the sequence of multiples of (9), so \(a_n=9n\). For (n=1), the first term should be (9).
यह (9) के गुणजों का अनुक्रम है, इसलिए \(a_n=9n\)। (n=1) पर पहला पद (9) मिलना चाहिए।
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If \(a_n=12-5n\), what is \(a_4\)?
C. (-8)
(a_4=12-5(4)=-8). Do not worry if subtraction gives a negative answer.
The correct answer is C. (-8). (a_4=12-5(4)=-8). Do not worry if subtraction gives a negative answer.
(a_4=12-5(4)=-8)। घटाव करते समय ऋणात्मक उत्तर से न डरें।
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What is the (n)th term of the sequence \(5,12,21,32,\ldots\)?
A. \(n^2+4n\)
Putting \(n^2+4n\) gives (5,12,21,32). Check the rule on the first four terms.
The correct answer is A. \(n^2+4n\). Putting \(n^2+4n\) gives (5,12,21,32). Check the rule on the first four terms.
\(n^2+4n\) रखने पर (5,12,21,32) मिलते हैं। पहले चार पदों पर नियम जांचें।
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If \(a_n=3\cdot4^{n-1}\), what is \(a_4\)?
C. (192)
\(a_4=3\cdot4^3=192\). In a geometric rule, the exponent is (n-1).
The correct answer is C. (192). \(a_4=3\cdot4^3=192\). In a geometric rule, the exponent is (n-1).
\(a_4=3\cdot4^3=192\)। गुणोत्तर नियम में घात (n-1) होती है।
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In the sequence \(14,18,22,26,\ldots\), what is (n) for \(a_n=70\)?
C. (15)
(a_n=14+(n-1)4=4n+10), so (4n+10=70) gives (n=15). Set the rule equal to the given term.
The correct answer is C. (15). (a_n=14+(n-1)4=4n+10), so (4n+10=70) gives (n=15). Set the rule equal to the given term.
(a_n=14+(n-1)4=4n+10), इसलिए (4n+10=70) से (n=15)। नियम को दिए पद के बराबर रखें।
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If \(a_n=n^2+2n-1\), what is the value of \(a_6\)?
B. (47)
(a_6=62+2(6)-1=47). First square, then add and subtract.
The correct answer is B. (47). (a_6=62+2(6)-1=47). First square, then add and subtract.
(a_6=62+2(6)-1=47)। पहले वर्ग करें फिर जोड़ और घटाव करें।
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In the geometric progression \(2,10,50,\ldots\), which term is (1250)?
B. (5)वाँ(5)th
The terms are (2,10,50,250,1250), so (1250) is the fifth term. Identify the powers in order.
The correct answer is B. (5)वाँ / (5)th. The terms are (2,10,50,250,1250), so (1250) is the fifth term. Identify the powers in order.
पद (2,10,50,250,1250) हैं, इसलिए (1250) पाँचवाँ पद है। घातों को क्रम से पहचानें।
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What is the (n)th term of the sequence \(6,16,26,36,\ldots\)?
A. (10n-4)
The first term is (6) and the difference is (10), so (a_n=6+(n-1)10=10n-4). Check by putting (n=1).
The correct answer is A. (10n-4). The first term is (6) and the difference is (10), so (a_n=6+(n-1)10=10n-4). Check by putting (n=1).
पहला पद (6) और अंतर (10) है, इसलिए (a_n=6+(n-1)10=10n-4)। पहले पद पर (n=1) रखकर जांचें।
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If \(a_n=\frac{5n-1}{2}\), what is \(a_7\)?
C. (17)
(a_7=\frac{5(7)-1}{2}=17). First simplify the numerator and then divide by (2).
The correct answer is C. (17). (a_7=\frac{5(7)-1}{2}=17). First simplify the numerator and then divide by (2).
(a_7=\frac{5(7)-1}{2}=17)। पहले अंश को सरल करें फिर (2) से भाग दें।
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What is the (n)th term of the sequence \(3,12,27,48,\ldots\)?
A. \(3n^2\)
The terms are (3(1)2,3(2)2,3(3)2,\ldots), so \(a_n=3n^2\). Identify both the square and the multiplier.
The correct answer is A. \(3n^2\). The terms are (3(1)2,3(2)2,3(3)2,\ldots), so \(a_n=3n^2\). Identify both the square and the multiplier.
पद (3(1)2,3(2)2,3(3)2,\ldots) हैं, इसलिए \(a_n=3n^2\)। वर्ग और गुणक दोनों पहचानें।
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If \(a_n=11n+2\), what is the value of \(a_4+a_6\)?
B. (110)
\(a_4=46\) and \(a_6=68\), so the sum is (114). Find both terms separately before choosing the option.
The correct answer is B. (110). \(a_4=46\) and \(a_6=68\), so the sum is (114). Find both terms separately before choosing the option.
\(a_4=46\) और \(a_6=68\), इसलिए योग (114) है। सही विकल्प चुनने से पहले दोनों पद अलग निकालें।
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In the sequence \(7,14,28,56,\ldots\), which term is (448)?
C. (7)वाँ(7)th
The terms are (7,14,28,56,112,224,448), so (448) is the seventh term. In a geometric progression, multiply by the same ratio each time.
The correct answer is C. (7)वाँ / (7)th. The terms are (7,14,28,56,112,224,448), so (448) is the seventh term. In a geometric progression, multiply by the same ratio each time.
पद (7,14,28,56,112,224,448) हैं, इसलिए (448) सातवाँ पद है। गुणोत्तर श्रेढ़ी में हर बार समान अनुपात से गुणा करें।
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If \(a_n=2n^2+3n\), what is \(a_5\)?
C. (65)
(a_5=2(5)2+3(5)=65). Calculate the square first and then add the remaining term.
The correct answer is C. (65). (a_5=2(5)2+3(5)=65). Calculate the square first and then add the remaining term.
(a_5=2(5)2+3(5)=65)। वर्ग की गणना पहले करें फिर बाकी पद जोड़ें।
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What is the (n)th term of the sequence \(40,35,30,25,\ldots\)?
A. (45-5n)
The first term is (40) and the difference is (-5), so (a_n=40+(n-1)(-5)=45-5n). In a decreasing sequence, take the difference as negative.
The correct answer is A. (45-5n). The first term is (40) and the difference is (-5), so (a_n=40+(n-1)(-5)=45-5n). In a decreasing sequence, take the difference as negative.
पहला पद (40) और अंतर (-5) है, इसलिए (a_n=40+(n-1)(-5)=45-5n)। घटती श्रेढ़ी में अंतर को ऋणात्मक लें।
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If \(a_n=\frac{n^2+n}{2}\), what is \(a_{10}\)?
C. (55)
\(a_{10}=\frac{100+10}{2}=55\). Simplify the numerator first and then divide by (2).
The correct answer is C. (55). \(a_{10}=\frac{100+10}{2}=55\). Simplify the numerator first and then divide by (2).
\(a_{10}=\frac{100+10}{2}=55\)। अंश को पहले सरल करें फिर (2) से भाग दें।
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If \(a_n=5\cdot2^{n-1}\), what is the value of \(a_6\)?
C. (160)
\(a_6=5\cdot2^5=160\). In a geometric rule, the exponent is (n-1).
The correct answer is C. (160). \(a_6=5\cdot2^5=160\). In a geometric rule, the exponent is (n-1).
\(a_6=5\cdot2^5=160\)। गुणोत्तर नियम में घात (n-1) होती है।
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