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