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254 questions tagged with nth_term.
If \(a_n=7-3n\), what is the (22)nd term of the AP?
A. (-59)
\(a_{22}=7-3\times22=-59\)। घटते प्रत्यक्ष सूत्र में ऋण चिह्न पर विशेष ध्यान दें। / \(a_{22}=7-3\times22=-59\). Pay special attention to the negative sign in a decreasing direct formula.
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If the (n)th term of an AP is given by \(a_n=4n-1\), what is \(a_{30}\)?
B. (119)
(n=30) रखने पर \(a_{30}=4\times30-1=119\)। प्रत्यक्ष सूत्र में केवल सही (n) रखें। / Putting (n=30), \(a_{30}=4\times30-1=119\). In a direct formula, substitute the correct (n).
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Find the (20)th term of the AP \(2.5,5,7.5,\ldots\).
B. (50)
यहां (a=2.5), (d=2.5), इसलिए \(a_{20}=2.5+19\times2.5=50\)। दशमलव AP में समान गुणन का ध्यान रखें। / Here (a=2.5), (d=2.5), so \(a_{20}=2.5+19\times2.5=50\). In decimal APs, keep multiplication exact.
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In an AP, \(a_3=11\) and (d=6). What is \(a_{17}\)?
B. (95)
(a_{17}=a_3+(17-3)d=11+14\times6=95)। किसी ज्ञात पद से सीधे आगे बढ़ना आसान है। / (a_{17}=a_3+(17-3)d=11+14\times6=95). Moving directly from a known term is easier.
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The first term of an AP is (18) and the (16)th term is (93). What is the common difference?
A. (5)
(93=18+15d), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा। / (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
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What will be the (15)th term of the AP \(100,92,84,\ldots\)?
D. (-12)
यहां (d=-8), इसलिए (a_{15}=100+14(-8)=-12)। बड़े घटते अंतर में गुणा पहले करें। / Here (d=-8), so (a_{15}=100+14(-8)=-12). In large decreasing differences, multiply first.
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In an AP, \(a_4=14\) and \(a_{12}=46\). What is the value of \(a_{20}\)?
C. (78)
\(d=\frac{46-14}{12-4}=4\), इसलिए \(a_{20}=46+8\times4=78\)। पास वाले ज्ञात पद से आगे बढ़ना तेज तरीका है। / \(d=\frac{46-14}{12-4}=4\), so \(a_{20}=46+8\times4=78\). Moving from the nearest known term is a faster method.
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If the (10)th term of an AP is (41) and the (20)th term is (81), what is its common difference?
C. (4)
दो पदों का अंतर (81-41=40) है और पद संख्या का अंतर (10), इसलिए (d=4)। \(दो ज्ञात पदों में (d=\frac{\)पदों का अंतर}{स्थान का अंतर}) लगाएं। \(/ The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
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What is the (31)st term of the AP \(-4,1,6,\ldots\)?
B. (146)
यहां (a=-4), (d=5), इसलिए \(a_{31}=-4+30\times5=146\)। ऋणात्मक पहले पद को सावधानी से जोड़ें। / Here (a=-4), (d=5), so \(a_{31}=-4+30\times5=146\). Add the negative first term carefully.
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Which term of the AP \(3,8,13,\ldots\) is (88)?
A. (18)वां(18)th
(88=3+(n-1)5) से (85=5(n-1)), अतः (n=18)। पद संख्या के प्रश्न में दिए पद को \(a_n\) मानें। / From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
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The (6)th term of an AP is (23) and the common difference is (5). What is the first term?
D. (-2)
(23=a+5d=a+25), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है। / (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
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In an AP, (a=5), (d=7), and \(a_n=103\). What is the value of (n)?
C. (15)
(103=5+(n-1)7) से (98=7(n-1)), अतः (n=15)। पद संख्या निकालते समय अंत में (1) जोड़ना न भूलें। / From (103=5+(n-1)7), (98=7(n-1)), so (n=15). When finding the term number, remember to add (1) at the end.
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Find the (25)th term of the AP \(12,9,6,\ldots\).
B. (-60)
यहां (a=12) और (d=-3), इसलिए (a_{25}=12+24(-3)=-60)। घटती श्रेणी में (d) का चिन्ह ध्यान रखें। / Here (a=12) and (d=-3), so (a_{25}=12+24(-3)=-60). Keep the sign of (d) carefully in decreasing APs.
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If the first term of an AP is (7) and the common difference is (4), what is its (18)th term?
A. (75)
सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए। / Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
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Find the (6)th term of the AP \(\frac{4}{5},\frac{9}{5},\frac{14}{5},\frac{19}{5},\ldots\).
B. \(\frac{29}{5}\)
यहाँ (d=1) है इसलिए \(a_6=\frac{4}{5}+5=\frac{29}{5}\)। पूर्ण संख्या को समान हर वाली भिन्न में बदलें। / Here (d=1), so \(a_6=\frac{4}{5}+5=\frac{29}{5}\). Convert the whole number to a fraction with the same denominator.
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What is the (40)th term of the AP \(14,14,14,14,\ldots\)?
B. (14)
यहाँ (d=0) है इसलिए हर पद (14) रहेगा। स्थिर एपी में \(a_n=a\) होता है। / Here (d=0), so every term remains (14). In a constant AP, \(a_n=a\).
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If \(a_9=70\) and (d=3), what is the (15)th term?
C. (88)
(15)वाँ पद (9)वें पद से (6d) आगे है इसलिए (70+18=88)। निकट पदों में यह विधि सरल है। / The (15)th term is (6d) after the (9)th term, so (70+18=88). This method is simple for nearby terms.
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What is the (28)th term of the AP \(9,15,21,27,\ldots\)?
B. (171)
यहाँ (d=6) है इसलिए \(a_{28}=9+27\times6=171\)। (28)वें पद के लिए (27d) जोड़ें। / Here (d=6), so \(a_{28}=9+27\times6=171\). For the (28)th term, add (27d).
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If \(a_1=22\) and (d=13), what is the (5)th term?
C. (74)
\(a_5=22+4\times13=74\)। \(a_1\) को प्रथम पद माना जाता है। / \(a_5=22+4\times13=74\). \(a_1\) is treated as the first term.
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Find the (14)th term of the AP \(33,29,25,21,\ldots\).
B. (-19)
यहाँ (d=-4) है इसलिए (a_{14}=33+13(-4)=-19)। (13) बार (-4) जोड़ें। / Here (d=-4), so (a_{14}=33+13(-4)=-19). Add (-4) thirteen times.
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What is the (16)th term of the AP \(6,17,28,39,\ldots\)?
B. (171)
यहाँ (d=11) है इसलिए \(a_{16}=6+15\times11=171\)। (16)वें पद के लिए (15) अंतर जोड़ें। / Here (d=11), so \(a_{16}=6+15\times11=171\). For the (16)th term, add (15) differences.
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If (a=120), (d=-9), and (n=13), find \(a_n\).
B. (12)
(a_{13}=120+12(-9)=12)। पहले \(12\times9\) घटाएं। / (a_{13}=120+12(-9)=12). First subtract \(12\times9\).
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What is the (18)th term of the AP \(-15,-9,-3,3,\ldots\)?
C. (87)
यहाँ (d=6) है इसलिए \(a_{18}=-15+17\times6=87\)। ऋणात्मक प्रथम पद को सही जोड़ें। / Here (d=6), so \(a_{18}=-15+17\times6=87\). Add the negative first term correctly.
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Find the (24)th term of the AP \(12,17,22,27,\ldots\).
B. (127)
यहाँ (d=5) है इसलिए \(a_{24}=12+23\times5=127\)। (24)वें पद के लिए (23d) जोड़ें। / Here (d=5), so \(a_{24}=12+23\times5=127\). For the (24)th term, add (23d).
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If \(a_8=44\) and (d=-2), what is the (12)th term?
B. (36)
(12)वाँ पद (8)वें पद से (4d) आगे है इसलिए (44+4(-2)=36)। ऋणात्मक अंतर को ध्यान से जोड़ें। / The (12)th term is (4d) after the (8)th term, so (44+4(-2)=36). Add the negative difference carefully.
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What is the (21)st term of the AP \(7,16,25,34,\ldots\)?
B. (187)
यहाँ (d=9) है इसलिए \(a_{21}=7+20\times9=187\)। (21)वें पद तक (20) अंतर जुड़ते हैं। / Here (d=9), so \(a_{21}=7+20\times9=187\). Up to the (21)st term, (20) differences are added.
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If an AP has (a=2.5), (d=2.5), and (n=10), what is \(a_n\)?
B. (25.0)
\(a_{10}=2.5+9\times2.5=25.0\)। दशमलव को सामान्य संख्या की तरह रखें। / \(a_{10}=2.5+9\times2.5=25.0\). Treat decimals like ordinary numbers.
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Find the (11)th term of the AP \(48,42,36,30,\ldots\).
B. (-12)
यहाँ (d=-6) है इसलिए (a_{11}=48+10(-6)=-12)। (11)वें पद के लिए (10d) जोड़ें। / Here (d=-6), so (a_{11}=48+10(-6)=-12). For the (11)th term, add (10d).
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If \(a_2=12\) and (d=9), what is the (7)th term?
B. (57)
(7)वाँ पद (2)रे पद से (5d) आगे है इसलिए (12+45=57)। दिए पद से आगे बढ़कर हल करें। / The (7)th term is (5d) after the (2)nd term, so (12+45=57). Solve by moving forward from the given term.
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What is the (9)th term of the AP \(18,28,38,48,\ldots\)?
C. (98)
यहाँ (d=10) है इसलिए \(a_9=18+8\times10=98\)। (9)वें पद तक (8) अंतर जुड़ते हैं। / Here (d=10), so \(a_9=18+8\times10=98\). Up to the (9)th term, (8) differences are added.
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