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3683 questions tagged with sequences.
Which is the (n)th term of the sequence \(8,21,40,65,96,\ldots\)?
C. \(3n^2+4n+1\)
दिए गए पद \(3n^2+4n+1\) से मिलते हैं। विकल्पों को पहले तीन पदों पर जांचना सुरक्षित तरीका है। / The given terms match \(3n^2+4n+1\). Testing options on the first three terms is a safe method.
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If \(a_n=35-6n\), which term is equal to (-43)?
B. (13)वां(13)th
(35-6n=-43) से (6n=78), इसलिए (n=13)। ऋणात्मक पदों में चिन्हों पर ध्यान दें। / From (35-6n=-43), (6n=78), so (n=13). Be careful with signs in negative terms.
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What is the (n)th term of the sequence \(5,17,37,65,101,\ldots\)?
A. \(4n^2+1\)
दूसरे अंतर (8) हैं और \(4n^2+1\) सभी शुरुआती पद देता है। दूसरे अंतर का आधा \(n^2\) का गुणांक होता है। / The second differences are (8), and \(4n^2+1\) gives all starting terms. Half of the second difference is the coefficient of \(n^2\).
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If \(a_n=2n^2+9n-11\), what is the value of \(a_{10}-a_4\)?
B. (204)
\(a_{10}=279\) और \(a_4=75\), इसलिए अंतर (204) है। दोनों पद अलग निकालकर घटाएं। / \(a_{10}=279\) and \(a_4=75\), so the difference is (204). Find both terms separately before subtracting.
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What is the (6)th term of the sequence \(6,30,150,750,\ldots\)?
A. (18750)
यह गुणोत्तर श्रेणी है और \(a_6=6\cdot5^5=18750\)। गुणोत्तर श्रेणी में घात (n-1) होती है। / This is a geometric sequence and \(a_6=6\cdot5^5=18750\). In a geometric sequence, the exponent is (n-1).
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If \(a_n=11n-15\), what is \(a_{2r-1}\)?
A. (22r-26)
(n=2r-1) रखने पर (a_{2r-1}=11(2r-1)-15=22r-26)। सूचकांक का पूरा व्यंजक प्रतिस्थापित करें। / Putting (n=2r-1), (a_{2r-1}=11(2r-1)-15=22r-26). Substitute the whole expression used as the index.
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Which is the (n)th term of the sequence \(9,26,51,84,125,\ldots\)?
B. \(4n^2+5n\)
पद \(4n^2+5n\) से मिलते हैं। द्विघात पैटर्न में विकल्पों को पहले तीन पदों पर जांचें। / The terms match \(4n^2+5n\). In a quadratic pattern, test the options on the first three terms.
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In an arithmetic sequence, \(a_6=47\) and \(a_{13}=110\). What is its (n)th term?
B. (9n-7)
(7d=63) से (d=9) और \(a_1=2\), इसलिए \(a_n=9n-7\)। दो दिए पदों से पहले सामान्य अंतर निकालें। / From (7d=63), (d=9) and \(a_1=2\), so \(a_n=9n-7\). From two given terms, find the common difference first.
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If \(a_n=7n^2-3n+5\), what is the value of \(a_6\)?
A. (239)
(a_6=7(6)2-3(6)+5=239)। वर्ग वाले पद में पहले \(n^2\) निकालें। / (a_6=7(6)2-3(6)+5=239). In a squared term, calculate \(n^2\) first.
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What is the (n)th term of the sequence \(17,25,33,41,\ldots\)?
C. (8n+9)
पहला पद (17) और अंतर (8) है, इसलिए (a_n=17+(n-1)8=8n+9)। समान्तर श्रेणी में (n-1) अंतर जुड़ते हैं। / The first term is (17) and the difference is (8), so (a_n=17+(n-1)8=8n+9). In an arithmetic sequence, (n-1) differences are added.
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What is the (n)th term of the sequence \(81,27,9,3,1,\ldots\)?
C. (81\left\(\frac{1}{3}\right\)^{n-1})
हर पद \(\frac{1}{3}\) गुना हो रहा है इसलिए (a_n=81\left\(\frac{1}{3}\right\)^{n-1})। पहले पद को सुरक्षित रखकर (n-1) घात लगाएं। / Each term is multiplied by \(\frac{1}{3}\), so (a_n=81\left\(\frac{1}{3}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
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The (n)th term of an arithmetic sequence is \(a_n=12n-7\). What is the common difference?
B. (12)
\(a_n=12n-7\) में (n) का गुणांक (12) है, इसलिए सामान्य अंतर (12) है। रैखिक (n)वें पद में (n) का गुणांक अंतर देता है। / In \(a_n=12n-7\), the coefficient of (n) is (12), so the common difference is (12). In a linear (n)th term, the coefficient of (n) gives the difference.
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If (a_n=n(n+4)), which term is (77)?
B. (7)वां(7)th
(n=7) रखने पर (7(7+4)=77)। विकल्पों को सीधे जांचना तेज तरीका हो सकता है। / Putting (n=7), (7(7+4)=77). Directly testing the options can be a quick method.
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Which is the (n)th term of the sequence \(5,7,11,19,35,\ldots\)?
A. \(2^n+3\)
पद \(2+3,4+3,8+3,\ldots\) हैं इसलिए \(a_n=2^n+3\)। घातीय पैटर्न में स्थिर जोड़ को पहचानें। / The terms are \(2+3,4+3,8+3,\ldots\), so \(a_n=2^n+3\). In exponential patterns, identify the constant addition.
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If \(a_n=5n+14\), what is \(a_{4p+2}\)?
A. (20p+24)
(n=4p+2) रखने पर (5(4p+2)+14=20p+24)। सूचकांक में दिया पूरा व्यंजक प्रतिस्थापित करें। / Putting (n=4p+2), (5(4p+2)+14=20p+24). Substitute the whole expression given in the index.
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What is the (n)th term of the sequence \(12,28,50,78,112,\ldots\)?
B. \(3n^2+7n+2\)
दूसरे अंतर (6) हैं और \(3n^2+7n+2\) शुरुआती पद देता है। द्विघात नियम में दूसरे अंतर का आधा \(n^2\) का गुणांक होता है। / The second differences are (6), and \(3n^2+7n+2\) gives the starting terms. In a quadratic rule, half of the second difference is the coefficient of \(n^2\).
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If \(a_n=40-7n\), when will \(a_n=5\)?
B. (5)वां(5)th
(40-7n=5) से (7n=35), इसलिए (n=5)। समीकरण बनाकर पद संख्या निकालें। / From (40-7n=5), (7n=35), so (n=5). Form an equation to find the term number.
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Which is the (n)th term of the sequence \(6,24,54,96,150,\ldots\)?
A. \(6n^2\)
पद \(6\cdot1^2,6\cdot2^2,6\cdot3^2,\ldots\) हैं इसलिए \(a_n=6n^2\)। वर्ग पैटर्न के गुणांक को पहचानें। / The terms are \(6\cdot1^2,6\cdot2^2,6\cdot3^2,\ldots\), so \(a_n=6n^2\). Identify the coefficient of the square pattern.
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If \(a_n=3n^2+4n\), what is the value of \(a_7-a_4\)?
C. (111)
\(a_7=175\) और \(a_4=64\), इसलिए अंतर (111) है। घटाने से पहले दोनों पद सही निकालें। / \(a_7=175\) and \(a_4=64\), so the difference is (111). Find both terms correctly before subtracting.
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What is the (25)th term of the sequence \(18,35,52,69,\ldots\)?
A. (426)
पहला पद (18) और अंतर (17) है, इसलिए \(a_{25}=18+24\cdot17=426\)। (25)वें पद में (24) अंतर जुड़ते हैं। / The first term is (18) and the difference is (17), so \(a_{25}=18+24\cdot17=426\). The (25)th term includes (24) differences.
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A sequence has \(a_n=4n^2-9n+7\). What is the value of \(a_{10}-a_3\)?
C. (301)
\(a_{10}=317\) और \(a_3=16\), इसलिए अंतर (301) है। दोनों पद अलग-अलग निकालकर घटाएं। / \(a_{10}=317\) and \(a_3=16\), so the difference is (301). Find both terms separately and subtract.
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What is the (n)th term of the sequence \(24,12,6,3,\frac{3}{2},\ldots\)?
C. (24\left\(\frac{1}{2}\right\)^{n-1})
हर पद आधा हो रहा है इसलिए (a_n=24\left\(\frac{1}{2}\right\)^{n-1})। गुणोत्तर श्रेणी में घात (n-1) से शुरू होती है। / Each term is halved, so (a_n=24\left\(\frac{1}{2}\right\)^{n-1}). In a geometric sequence, the exponent starts with (n-1).
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If \(a_n=n^2+10\), which term is (131)?
B. (11)वां(11)th
\(n^2+10=131\) से \(n^2=121\), इसलिए (n=11)। पद संख्या धन पूर्णांक ही ली जाती है। / From \(n^2+10=131\), \(n^2=121\), so (n=11). A term number is taken as a positive integer.
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Which is the (n)th term of the sequence \(3,-6,9,-12,15,\ldots\)?
B. (3(-1)^{n+1}n)
विषम (n) पर पद धनात्मक और सम (n) पर ऋणात्मक है, इसलिए (a_n=3(-1)^{n+1}n)। वैकल्पिक चिन्ह में पहले (n=1) पर जांचें। / For odd (n), terms are positive and for even (n), terms are negative, so (a_n=3(-1)^{n+1}n). In alternating signs, test first at (n=1).
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If \(a_n=7\cdot2^{n-1}-3\), what is the value of \(a_5\)?
C. (109)
\(a_5=7\cdot2^4-3=109\)। (n-1) वाली घात को सही रखें। / \(a_5=7\cdot2^4-3=109\). Keep the exponent (n-1) correctly.
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What is the (n)th term of the sequence \(8,21,40,65,96,\ldots\)?
B. \(3n^2+4n+1\)
दूसरे अंतर (6) हैं और \(3n^2+4n+1\) सभी शुरुआती पद देता है। द्विघात श्रेणी में विकल्पों को पहले तीन पदों पर जांचें। / The second differences are (6), and \(3n^2+4n+1\) gives all starting terms. In a quadratic sequence, test options on the first three terms.
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If (a_n=\frac{n(n+5)}{3}), what is the value of \(a_{12}\)?
C. (68)
(a_{12}=\frac{12(17)}{3}=68)। भिन्न में पहले सरल करना गणना आसान बनाता है। / (a_{12}=\frac{12(17)}{3}=68). Simplifying first makes fraction calculation easier.
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In the sequence \(19,31,43,55,\ldots\), which term is (151)?
B. (12)वां(12)th
(19+(n-1)12=151) से (n-1=11), इसलिए (n=12)। पद संख्या निकालते समय (n-1) को न भूलें। / From (19+(n-1)12=151), (n-1=11), so (n=12). Do not forget (n-1) while finding the term number.
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If \(a_n=6n-8\), what is \(a_{3n-2}\)?
B. (18n-20)
(n) की जगह (3n-2) रखने पर (6(3n-2)-8=18n-20)। पूरे सूचकांक को ब्रैकेट में रखकर हल करें। / Replacing (n) by (3n-2), (6(3n-2)-8=18n-20). Put the whole index in brackets while solving.
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Which is the (n)th term of the sequence \(1,7,17,31,49,\ldots\)?
A. \(2n^2-1\)
दिए गए पद \(2n^2-1\) से मिलते हैं। पहले पद (1) और दूसरे पद (7) से विकल्प जांचें। / The given terms match \(2n^2-1\). Test options using the first term (1) and the second term (7).
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