Level 65 • 50/50 questions • 35 seconds per question.
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What is the (28)th term of the AP \(4,11,18,\ldots\)?
B. (193)
(a=4) और (d=7) हैं इसलिए \(a_{28}=4+27\times7=193\)। परीक्षा में पद संख्या से (1) घटाना न भूलें। / (a=4) and (d=7) so \(a_{28}=4+27\times7=193\). In exams remember to subtract (1) from the term number.
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Find the (17)th term of the AP \(38,33,28,\ldots\).
A. (-42)
यहां (a=38) और (d=-5) है इसलिए (a_{17}=38+16(-5)=-42)। घटती श्रेणी में (d) को ऋणात्मक लें। / Here (a=38) and (d=-5) so (a_{17}=38+16(-5)=-42). In a decreasing AP take (d) as negative.
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If (a=13), (d=6), and \(a_n=121\), what is the value of (n)?
C. (19)
(121=13+(n-1)6) से (108=6(n-1)) इसलिए (n=19)। (n-1) मिलने के बाद (1) जरूर जोड़ें। / From (121=13+(n-1)6), (108=6(n-1)) so (n=19). After finding (n-1), add (1).
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The (9)th term of an AP is (47) and the common difference is (4). What is the first term?
D. (15)
\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं। / From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
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Which term of the AP \(21,29,37,\ldots\) is (149)?
C. (17)वां(17)th
(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें। / From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
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What will be the (24)th term of the AP \(-15,-9,-3,\ldots\)?
B. (123)
यहां (a=-15) और (d=6) है इसलिए \(a_{24}=-15+23\times6=123\)। ऋणात्मक पहले पद को अलग से ध्यान में रखें। / Here (a=-15) and (d=6) so \(a_{24}=-15+23\times6=123\). Keep the negative first term in mind.
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If \(a_6=31\) and \(a_{14}=79\), what is the common difference of the AP?
A. (6)
\(d=\frac{79-31}{14-6}=6\)। दो पदों में पदों का अंतर स्थानों के अंतर से भाग दें। / \(d=\frac{79-31}{14-6}=6\). Divide the difference of terms by the difference of positions.
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In an AP, \(a_5=27\) and \(a_{13}=67\). What is the value of \(a_{21}\)?
D. (107)
\(d=\frac{67-27}{13-5}=5\) और \(a_{21}=67+8\times5=107\)। निकट ज्ञात पद से आगे बढ़ना तेज होता है। / \(d=\frac{67-27}{13-5}=5\) and \(a_{21}=67+8\times5=107\). Moving from the nearer known term is faster.
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What is the (12)th term of the AP \(96,87,78,\ldots\)?
A. (-3)
(d=-9) है इसलिए (a_{12}=96+11(-9)=-3)। बड़े घटते अंतर में चिन्ह गलती से न बदलें। / (d=-9) so (a_{12}=96+11(-9)=-3). Do not accidentally change the sign in a large decreasing difference.
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The first term of an AP is (25) and the (18)th term is (93). What is the common difference?
C. (4)
(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है। / From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
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If \(a_4=19\) and (d=7), what is \(a_{18}\)?
B. (117)
(a_{18}=a_4+(18-4)d=19+14\times7=117)। ज्ञात पद से सीधे अंतर जोड़ें। / (a_{18}=a_4+(18-4)d=19+14\times7=117). Add the gap directly from the known term.
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Find the (19)th term of the AP \(1.2,2.7,4.2,\ldots\).
D. (28.2)
यहां (a=1.2) और (d=1.5) है इसलिए \(a_{19}=1.2+18\times1.5=28.2\)। दशमलव में गुणा सावधानी से करें। / Here (a=1.2) and (d=1.5) so \(a_{19}=1.2+18\times1.5=28.2\). Multiply decimals carefully.
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If \(a_n=5n+8\), what is the value of \(a_{26}\)?
C. (138)
(n=26) रखने पर \(a_{26}=5\times26+8=138\)। प्रत्यक्ष सूत्र में सही पद संख्या रखें। / Putting (n=26), \(a_{26}=5\times26+8=138\). Substitute the correct term number in the direct formula.
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If \(a_n=82-4n\), what will be the (23)rd term of the AP?
A. (-10)
\(a_{23}=82-4\times23=-10\)। घटते प्रत्यक्ष सूत्र में घटाव को ध्यान से करें। / \(a_{23}=82-4\times23=-10\). Do subtraction carefully in a decreasing direct formula.
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What is the (31)st term of the AP \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\ldots\)?
B. \(\frac{63}{4}\)
यहां \(a=\frac{3}{4}\) और \(d=\frac{1}{2}\) है इसलिए \(a_{31}=\frac{3}{4}+30\cdot\frac{1}{2}=\frac{63}{4}\)। भिन्नों में समान हर बनाएं। / Here \(a=\frac{3}{4}\) and \(d=\frac{1}{2}\) so \(a_{31}=\frac{3}{4}+30\cdot\frac{1}{2}=\frac{63}{4}\). Use a common denominator for fractions.
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The (10)th term of an AP is (62) and (d=5). What is \(a_1\)?
D. (17)
\(62=a+9\times5\) से (a=17)। (10)वें पद से पहले पद तक (9d) घटता है। / From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
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Which term of the AP \(14,23,32,\ldots\) is (185)?
C. (20)वां(20)th
(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं। / From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
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What will be the (22)nd term of the AP \(-32,-25,-18,\ldots\)?
B. (115)
(a=-32) और (d=7) हैं इसलिए \(a_{22}=-32+21\times7=115\)। ऋणात्मक आरंभ में जोड़ते समय सावधान रहें। / (a=-32) and (d=7) so \(a_{22}=-32+21\times7=115\). Be careful while adding from a negative start.
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If \(a_8=44\) and \(a_{18}=104\), what is \(a_{28}\)?
D. (164)
\(d=\frac{104-44}{10}=6\) इसलिए \(a_{28}=104+10\times6=164\)। समान स्थान अंतर होने पर समान पद अंतर जोड़ें। / \(d=\frac{104-44}{10}=6\) so \(a_{28}=104+10\times6=164\). Add the same term difference for equal position gaps.
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If the first term of an AP is (16) and \(a_{26}=116\), what is (d)?
A. (4)
(116=16+25d) से (100=25d) इसलिए (d=4)। (26)वें पद में (d) (25) बार जुड़ता है। / From (116=16+25d), (100=25d) so (d=4). In the (26)th term, (d) is added (25) times.
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Which is the first negative term of the AP \(72,66,60,\ldots\)?
B. (14)वां(14)th
(a_n=72+(n-1)(-6)=78-6n)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है। / (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
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In the AP \(5,12,19,\ldots\), what is the greatest term less than (150)?
A. (145)
पद (5+7(n-1)) के रूप में हैं। (150) से कम सबसे बड़ा ऐसा पद (145) है। / The terms are of the form (5+7(n-1)). The greatest such term less than (150) is (145).
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If \(a_n=3n-2\), what are the first term and common difference?
D. (a=1,d=3)
(n=1) रखने पर \(a_1=1\) और (n) का गुणांक (3) ही (d) है। प्रत्यक्ष सूत्र से दोनों मान तुरंत मिलते हैं। / Putting (n=1), \(a_1=1\) and the coefficient of (n) is (d=3). The direct formula gives both values quickly.
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In an AP, (a=48) and (d=-3). Which term will be (0)?
C. (17)वां(17)th
(0=48+(n-1)(-3)) से (3(n-1)=48) इसलिए (n=17)। शून्य पद के लिए भी सामान्य सूत्र लगाएं। / From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
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In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
A. (74)
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है। / The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
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If in an AP \(a_{16}=91\) and (d=6), what is \(a_3\)?
D. (19)
\(a_3=a_{16}-13d=91-78=13\)। पीछे जाते समय स्थानों के अंतर को (d) से गुणा करके घटाएं। / \(a_3=a_{16}-13d=91-78=13\). While moving backward, multiply the position gap by (d) and subtract.
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B. (45.5) किमी(45.5) km
(a=3) और (d=2.5) हैं इसलिए \(a_{18}=3+17\times2.5=45.5\) किमी। शब्द-प्रश्न में पहला मान (a) होता है। / (a=3) and (d=2.5) so \(a_{18}=3+17\times2.5=45.5\) km. In word problems, the first value is (a).
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C. (62)
\(a_{20}=5+19\times3=62\)। यह एक पद की अंक संख्या है कुल अंक नहीं। / \(a_{20}=5+19\times3=62\). This is the mark value of one question, not the total marks.
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B. (69)
\(a_{16}=24+15\times3=69\)। (16)वीं पंक्ति तक अंतर (15) बार जुड़ता है। / \(a_{16}=24+15\times3=69\). Up to the (16)th row, the difference is added (15) times.
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A. (60) लीटर(60) litres
यह घटती समान्तर श्रेणी है जिसमें (a=180) और (d=-12) है। (a_{11}=180+10(-12)=60) लीटर। / This is a decreasing AP with (a=180) and (d=-12). (a_{11}=180+10(-12)=60) litres.
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D. (665)
\(a_{22}=350+21\times15=665\)। पहले दिन को \(a_1\) मानकर (21) अंतर जोड़ें। / \(a_{22}=350+21\times15=665\). Treat the first day as \(a_1\) and add (21) differences.
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C. (₹585)
शुल्क घट रहा है इसलिए (d=-35)। (a_{10}=900+9(-35)=585)। / The fee is decreasing so (d=-35). (a_{10}=900+9(-35)=585).
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If \(a_n=11n-4\), what is the value of \(a_{15}-a_9\)?
B. (66)
स्थान अंतर (15-9=6) है और (d=11) है इसलिए अंतर \(6\times11=66\)। ऐसे प्रश्न में दोनों पद अलग से निकालना जरूरी नहीं। / The position gap is (15-9=6) and (d=11), so the difference is \(6\times11=66\). You do not need to find both terms separately.
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In an AP, \(a_{12}=54\) and \(a_{20}=94\). What is the first term?
A. (-1)
\(d=\frac{94-54}{8}=5\) और \(a_1=54-11\times5=-1\)। पहले (d) निकालकर पीछे जाएं। / \(d=\frac{94-54}{8}=5\) and \(a_1=54-11\times5=-1\). Find (d) first and move backward.
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If the (12)th term of the AP \(y,y+6,y+12,\ldots\) is (89), what is the value of (y)?
D. (23)
\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें। / From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
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The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?
C. (19)
(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें। / From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
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If \(a_9=42\) and \(a_{16}=77\), what is \(a_{23}\)?
D. (112)
\(d=\frac{77-42}{7}=5\) इसलिए \(a_{23}=77+7\times5=112\)। समान दूरी के पदों में समान वृद्धि होती है। / \(d=\frac{77-42}{7}=5\) so \(a_{23}=77+7\times5=112\). Equally spaced terms have equal increases.
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In an AP, (a=9) and \(d=\frac{5}{2}\). What is \(a_{17}\)?
B. (49)
\(a_{17}=9+16\cdot\frac{5}{2}=49\)। भिन्न वाले (d) में पहले गुणा सरल करें। / \(a_{17}=9+16\cdot\frac{5}{2}=49\). With fractional (d), simplify multiplication first.
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If \(a_n=7-2n\), which term will be (-35)?
A. (21)वां(21)th
(-35=7-2n) से (2n=42) इसलिए (n=21)। प्रत्यक्ष सूत्र में समीकरण सीधा हल करें। / From (-35=7-2n), (2n=42) so (n=21). Solve the direct formula equation directly.
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In an AP, \(a_{11}=40\) and \(a_{19}=72\). What is \(a_4\)?
C. (12)
\(d=\frac{72-40}{8}=4\) और \(a_4=40-7\times4=12\)। ज्ञात पद से पीछे जाने पर (d) घटाते जाएं। / \(d=\frac{72-40}{8}=4\) and \(a_4=40-7\times4=12\). When moving backward from a known term, subtract (d).
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In the AP \(17,24,31,\ldots\), \(a_n=136\). Find the value of (n).
B. (18)
(136=17+(n-1)7) से (119=7(n-1)) इसलिए (n=18)। पद संख्या पूर्णांक आनी चाहिए। / From (136=17+(n-1)7), (119=7(n-1)) so (n=18). The term number should be an integer.
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If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?
D. (2m+13)
((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें। / The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
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If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?
C. (75)
\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें। / \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
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The AP of multiples of (8) greater than (300) is \(304,312,320,\ldots\). What is its (25)th term?
A. (496)
यहां (a=304) और (d=8) है इसलिए \(a_{25}=304+24\times8=496\)। सीमा के बाद पहला सही गुणज चुनें। / Here (a=304) and (d=8) so \(a_{25}=304+24\times8=496\). Choose the first correct multiple after the limit.
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What is the last term among the positive multiples of (11) less than (500)?
B. (495)
(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक लें। / In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
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The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?
D. (299)
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें। / \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
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If \(a_{n+1}-a_n=9\) and \(a_6=48\), what is \(a_{20}\)?
C. (174)
यहां (d=9) है इसलिए \(a_{20}=48+14\times9=174\)। \(a_{n+1}-a_n\) समान्तर श्रेणी का सार्व अंतर होता है। / Here (d=9) so \(a_{20}=48+14\times9=174\). \(a_{n+1}-a_n\) is the common difference of the AP.
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In an AP, \(a_1+a_2=33\) and (d=5). What is \(a_{12}\)?
B. (69)
(a_1+a_2=a+(a+5)=33) से (a=14)। इसलिए \(a_{12}=14+11\times5=69\)। / From (a_1+a_2=a+(a+5)=33), (a=14). Therefore \(a_{12}=14+11\times5=69\).
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If in an AP \(a_6+a_{14}=100\), what is the value of \(a_{10}\)?
A. (50)
\(a_6\) और \(a_{14}\) के बीच का पद \(a_{10}\) है इसलिए \(a_{10}=\frac{100}{2}=50\)। समान दूरी वाले पदों का औसत बीच वाला पद होता है। / \(a_{10}\) is the middle term between \(a_6\) and \(a_{14}\), so \(a_{10}=\frac{100}{2}=50\). The average of equally spaced terms is the middle term.
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In the AP \(90,83,76,\ldots\), which is the last term greater than (20)?
D. (27)
(d=-7) है और पद \(90,83,76,\ldots,27,20\) आते हैं। (20) से बड़ा अंतिम पद (27) है। / (d=-7) and the terms go \(90,83,76,\ldots,27,20\). The last term greater than (20) is (27).
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