Level 66 • 50/50 questions • 35 seconds per question.
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What is the (23)rd term of the AP \(6,14,22,\ldots\)?
A. (182)
यहां (a=6) और (d=8) है इसलिए \(a_{23}=6+22\times8=182\)। परीक्षा में (n) की जगह (n-1) लगाना याद रखें। / Here (a=6) and (d=8) so \(a_{23}=6+22\times8=182\). Remember to use (n-1) instead of (n) in exams.
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Find the (18)th term of the AP \(84,78,72,\ldots\).
B. (-18)
यहां (d=-6) है इसलिए (a_{18}=84+17(-6)=-18)। घटती AP में सार्व अंतर को ऋणात्मक लें। / Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.
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If in an AP (a=17), (d=9), and \(a_n=170\), what is the value of (n)?
C. (18)
(170=17+(n-1)9) से (153=9(n-1)) इसलिए (n=18)। पद संख्या निकालते समय अंत में (1) जोड़ें। / From (170=17+(n-1)9), (153=9(n-1)) so (n=18). Add (1) at the end while finding the term number.
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The (12)th term of an AP is (71) and the common difference is (5). What is the first term?
D. (16)
\(71=a+11\times5\) से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं। / From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
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Which term of the AP \(9,17,25,\ldots\) is (201)?
C. (25)वां(25)th
(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है। / From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
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What will be the (21)st term of the AP \(-28,-20,-12,\ldots\)?
D. (132)
यहां (a=-28) और (d=8) है इसलिए \(a_{21}=-28+20\times8=132\)। ऋणात्मक पहले पद को जोड़ते समय सावधानी रखें। / Here (a=-28) and (d=8) so \(a_{21}=-28+20\times8=132\). Be careful while adding a negative first term.
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If \(a_7=36\) and \(a_{16}=90\), what is the common difference of the AP?
A. (6)
\(d=\frac{90-36}{16-7}=6\)। दो ज्ञात पदों में पदों का अंतर स्थानों के अंतर से भाग दें। / \(d=\frac{90-36}{16-7}=6\). Divide the difference of terms by the difference of positions.
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In an AP \(a_6=38\) and \(a_{15}=101\). What is \(a_{24}\)?
B. (164)
\(d=\frac{101-38}{15-6}=7\) इसलिए \(a_{24}=101+9\times7=164\)। निकट ज्ञात पद से आगे बढ़ना सरल होता है। / \(d=\frac{101-38}{15-6}=7\) so \(a_{24}=101+9\times7=164\). Moving forward from the nearer known term is easier.
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What will be the (13)th term of the AP \(120,109,98,\ldots\)?
C. (-12)
(d=-11) है इसलिए (a_{13}=120+12(-11)=-12)। बड़े ऋणात्मक अंतर में गुणा पहले करें। / (d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.
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The first term of an AP is (31) and \(a_{19}=139\). What is the common difference?
C. (6)
(139=31+18d) से (108=18d) इसलिए (d=6)। (19)वें पद के लिए (18d) जुड़ता है। / From (139=31+18d), (108=18d) so (d=6). For the (19)th term (18d) is added.
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If \(a_5=24\) and (d=8), what is the value of \(a_{19}\)?
B. (136)
(a_{19}=a_5+(19-5)d=24+14\times8=136)। ज्ञात पद से सीधे स्थान अंतर जोड़ें। / (a_{19}=a_5+(19-5)d=24+14\times8=136). Add the position gap directly from the known term.
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Find the (16)th term of the AP \(2.4,4.0,5.6,\ldots\).
C. (26.4)
यहां (a=2.4) और (d=1.6) है इसलिए \(a_{16}=2.4+15\times1.6=26.4\)। दशमलव गुणा में स्थान मूल्य ध्यान रखें। / Here (a=2.4) and (d=1.6) so \(a_{16}=2.4+15\times1.6=26.4\). Keep place value in mind while multiplying decimals.
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If \(a_n=6n+7\), what is \(a_{34}\)?
B. (211)
(n=34) रखने पर \(a_{34}=6\times34+7=211\)। प्रत्यक्ष सूत्र में केवल सही (n) रखें। / Putting (n=34), \(a_{34}=6\times34+7=211\). Substitute only the correct value of (n) in the direct formula.
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If \(a_n=95-5n\), what will be the (26)th term?
A. (-35)
\(a_{26}=95-5\times26=-35\)। घटते सूत्र में घटाव के बाद चिन्ह जांचें। / \(a_{26}=95-5\times26=-35\). In a decreasing formula check the sign after subtraction.
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What is the (28)th term of the AP \(\frac{2}{3},\frac{4}{3},2,\ldots\)?
B. \(\frac{56}{3}\)
यहां \(a=\frac{2}{3}\) और \(d=\frac{2}{3}\) है इसलिए \(a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}\)। भिन्नों में गुणन को पहले सरल करें। / Here \(a=\frac{2}{3}\) and \(d=\frac{2}{3}\) so \(a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}\). Simplify multiplication first in fractions.
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The (14)th term of an AP is (92) and (d=7). What is \(a_1\)?
A. (1)
\(92=a+13\times7\) से (a=1)। (14)वें पद से पहले पद तक (13d) घटता है। / From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.
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Which term of the AP \(26,35,44,\ldots\) is (206)?
C. (21)वां(21)st
(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें। / From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
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What will be the (20)th term of the AP \(-45,-36,-27,\ldots\)?
C. (126)
(a=-45) और (d=9) हैं इसलिए \(a_{20}=-45+19\times9=126\)। ऋणात्मक शुरूआत वाली बढ़ती AP में अंतिम जोड़ सावधानी से करें। / (a=-45) and (d=9) so \(a_{20}=-45+19\times9=126\). In an increasing AP starting negative add carefully at the end.
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If \(a_9=52\) and \(a_{17}=108\), what is \(a_{25}\)?
B. (164)
\(d=\frac{108-52}{17-9}=7\) इसलिए \(a_{25}=108+8\times7=164\)। समान स्थान अंतर पर पदों का अंतर भी समान रहता है। / \(d=\frac{108-52}{17-9}=7\) so \(a_{25}=108+8\times7=164\). Equal position gaps have equal term gaps in an AP.
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If the first term of an AP is (22) and \(a_{32}=177\), what is the common difference?
C. (5)
(177=22+31d) से (155=31d) और (d=5)। (32)वें पद में (31d) जुड़ता है। / From (177=22+31d), (155=31d) and (d=5). In the (32)nd term (31d) is added.
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Which is the first negative term of the AP \(105,98,91,\ldots\)?
C. (17)वां(17)th
(a_n=105+(n-1)(-7)=112-7n)। \(a_n<0\) से (n>16) इसलिए पहला ऋणात्मक पद (17)वां है। / (a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
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In the AP \(13,21,29,\ldots\), what is the greatest term less than (250)?
C. (245)
पद (13+8(n-1)) के रूप में हैं और (250) से कम सबसे बड़ा ऐसा पद (245) है। सीमा वाले प्रश्न में अगले पद से भी जांच करें। / The terms are of the form (13+8(n-1)) and the greatest such term less than (250) is (245). In limit questions check the next term too.
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If \(a_n=4n+11\), what are the first term and common difference?
A. (a=15,d=4)
(n=1) रखने पर \(a_1=15\) और (n) का गुणांक (4) ही (d) है। प्रत्यक्ष सूत्र से दोनों मान तुरंत मिलते हैं। / Putting (n=1), \(a_1=15\) and the coefficient of (n) is (d=4). The direct formula gives both values quickly.
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In an AP (a=63) and (d=-4). Which term will be (-1)?
C. (17)वां(17)th
(-1=63+(n-1)(-4)) से (64=4(n-1)) इसलिए (n=17)। ऋणात्मक लक्ष्य पद में चिन्हों को ध्यान से संभालें। / From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.
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In the AP \(7,12,17,\ldots\), what is the last term less than (180)?
C. (177)
पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा। / The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
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If in an AP \(a_{18}=130\) and (d=8), what is \(a_4\)?
A. (18)
\(a_4=a_{18}-14d=130-112=18\)। पीछे जाते समय स्थान अंतर को (d) से गुणा करके घटाएं। / \(a_4=a_{18}-14d=130-112=18\). While moving backward multiply the position gap by (d) and subtract.
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B. (110) किमी(110) km
यह AP है जिसमें (a=12) और (d=7) है। \(a_{15}=12+14\times7=110\) किमी। / This is an AP with (a=12) and (d=7). \(a_{15}=12+14\times7=110\) km.
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C. (122)
\(a_{18}=20+17\times6=122\)। यह एक स्तर के अंक हैं कुल अंक नहीं। / \(a_{18}=20+17\times6=122\). This is the score for one level not the total score.
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B. (128)
\(a_{25}=32+24\times4=128\)। (25)वीं शेल्फ तक अंतर (24) बार जुड़ता है। / \(a_{25}=32+24\times4=128\). Up to the (25)th shelf the difference is added (24) times.
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A. (96) लीटर(96) litres
यह घटती AP है जिसमें (a=240) और (d=-18) है। (a_9=240+8(-18)=96) लीटर। / This is a decreasing AP with (a=240) and (d=-18). (a_9=240+8(-18)=96) litres.
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B. (127)
\(a_{30}=40+29\times3=127\)। पहले दिन को \(a_1\) मानें दिन (0) नहीं। / \(a_{30}=40+29\times3=127\). Treat the first day as \(a_1\) not day (0).
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B. (₹2475)
\(a_{14}=1500+13\times75=2475\)। मासिक किराया पद है कुल भुगतान नहीं। / \(a_{14}=1500+13\times75=2475\). The monthly rent is the term not the total payment.
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If \(a_n=13n-6\), what is the value of \(a_{18}-a_{11}\)?
C. (91)
स्थान अंतर (18-11=7) और (d=13) है इसलिए अंतर \(7\times13=91\)। दोनों पद अलग से निकालना जरूरी नहीं। / The position gap is (18-11=7) and (d=13) so the difference is \(7\times13=91\). You do not need to find both terms separately.
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In an AP \(a_{10}=58\) and \(a_{22}=130\). What is the first term?
B. (4)
\(d=\frac{130-58}{22-10}=6\) और \(a_1=58-9\times6=4\)। पहले (d) निकालकर पीछे चलें। / \(d=\frac{130-58}{22-10}=6\) and \(a_1=58-9\times6=4\). Find (d) first and move backward.
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If the (19)th term of the AP \(z,z+5,z+10,\ldots\) is (112), what is (z)?
C. (22)
\(112=z+18\times5\) से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं। / From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
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The (n)th term of the AP \(73,68,63,\ldots\) is (-12). What is (n)?
C. (18)
(-12=73+(n-1)(-5)) से (85=5(n-1)) इसलिए (n=18)। घटती AP में ऋणात्मक लक्ष्य तक चिन्ह सही रखें। / From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.
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If \(a_8=47\) and \(a_{15}=103\), what is \(a_{22}\)?
C. (159)
\(d=\frac{103-47}{15-8}=8\) इसलिए \(a_{22}=103+7\times8=159\)। बराबर दूरी वाले पदों में समान अंतर जोड़ें। / \(d=\frac{103-47}{15-8}=8\) so \(a_{22}=103+7\times8=159\). Add equal term gaps for equally spaced positions.
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In an AP (a=12) and \(d=\frac{7}{2}\). What is \(a_{15}\)?
B. (61)
\(a_{15}=12+14\cdot\frac{7}{2}=61\)। भिन्न वाले (d) में गुणन को पहले सरल करें। / \(a_{15}=12+14\cdot\frac{7}{2}=61\). With fractional (d) simplify multiplication first.
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If \(a_n=10-3n\), which term will be (-44)?
C. (18)वां(18)th
(-44=10-3n) से (3n=54) इसलिए (n=18)। प्रत्यक्ष सूत्र में समीकरण को सीधे हल करें। / From (-44=10-3n), (3n=54) so (n=18). Solve the direct formula equation directly.
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In an AP \(a_{13}=65\) and \(a_{21}=113\). What is \(a_6\)?
C. (23)
\(d=\frac{113-65}{8}=6\) और \(a_6=65-7\times6=23\)। ज्ञात पद से पीछे जाने पर (d) घटाएं। / \(d=\frac{113-65}{8}=6\) and \(a_6=65-7\times6=23\). When moving backward from a known term subtract (d).
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In the AP \(18,27,36,\ldots\), \(a_n=189\). Find the value of (n).
B. (20)
(189=18+(n-1)9) से (171=9(n-1)) इसलिए (n=20)। पद संख्या के लिए पहले पद को घटाकर (d) से भाग दें। / From (189=18+(n-1)9), (171=9(n-1)) so (n=20). For term number subtract the first term and divide by (d).
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If the (r)th term of an AP is (3r-2) and (d=4), what is the ((r+6))th term?
C. (3r+22)
((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें। / The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
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If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?
C. (132)
\(d=\frac{90-27}{14-5}=7\) और \(a_{20}=90+6\times7=132\)। पहले (d) निकालें फिर आगे बढ़ें। / \(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
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The AP of multiples of (12) greater than (400) is \(408,420,432,\ldots\). What is its (18)th term?
A. (612)
यहां (a=408) और (d=12) है इसलिए \(a_{18}=408+17\times12=612\)। सीमा के बाद पहला सही गुणज चुनें। / Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
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What is the last term among the positive multiples of (13) less than (600)?
B. (598)
(13n<600) में सबसे बड़ा (n=46) है इसलिए पद \(13\times46=598\)। सीमा से कम सबसे बड़ा पूर्णांक लें। / In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
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The (n)th-term formula of the AP \(23,31,39,\ldots\) is \(a_n=8n+15\). What is the (36)th term?
C. (303)
\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं। / \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
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If \(a_{n+1}-a_n=11\) and \(a_7=58\), what is \(a_{17}\)?
D. (168)
यहां (d=11) है इसलिए \(a_{17}=58+10\times11=168\)। \(a_{n+1}-a_n\) ही सार्व अंतर होता है। / Here (d=11) so \(a_{17}=58+10\times11=168\). \(a_{n+1}-a_n\) is the common difference.
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In an AP \(a_1+a_2=41\) and (d=7). What is \(a_{10}\)?
C. (86)
(a_1+a_2=a+(a+7)=41) से (a=17)। इसलिए \(a_{10}=17+9\times7=80\)। / From (a_1+a_2=a+(a+7)=41), (a=17). Therefore \(a_{10}=17+9\times7=80\).
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If in an AP \(a_7+a_{19}=156\), what is the value of \(a_{13}\)?
C. (78)
\(a_7\) और \(a_{19}\) के बीच का पद \(a_{13}\) है इसलिए \(a_{13}=\frac{156}{2}=78\)। समान दूरी वाले पदों का औसत बीच वाला पद होता है। / \(a_{13}\) is the middle term between \(a_7\) and \(a_{19}\) so \(a_{13}=\frac{156}{2}=78\). The average of equally spaced terms is the middle term.
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In the AP \(128,119,110,\ldots\), which is the last term greater than (30)?
C. (38)
(d=-9) है और पद \(128,119,110,\ldots,38,29\) आते हैं। (30) से बड़ा अंतिम पद (38) है। / (d=-9) and the terms go \(128,119,110,\ldots,38,29\). The last term greater than (30) is (38).
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