Level 52 • 50/50 questions • 35 seconds per question.
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What is the common difference in the sequence \(6,13,20,27,\ldots\)?
C. (7)
लगातार पदों का अंतर (13-6=7) है। समान अंतर के लिए दूसरे पद से पहला पद घटाएं। / The difference between consecutive terms is (13-6=7). To find the common difference, subtract the first term from the second term.
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If an arithmetic progression has first term (8) and common difference (5), what is the (7)th term?
C. (38)
(a_7=8+(7-1)5=38)। (n)वें पद के लिए (a_n=a+(n-1)d) लगाएं। / (a_7=8+(7-1)5=38). Use (a_n=a+(n-1)d) for the (n)th term.
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What is the (n)th term of the arithmetic progression \(42,36,30,24,\ldots\)?
A. \(a_n=48-6n\)
पहला पद (42) और अंतर (-6) है इसलिए (a_n=42+(n-1)(-6)=48-6n)। घटती श्रेढ़ी में समान अंतर ऋणात्मक होता है। / The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). In a decreasing progression, the common difference is negative.
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If (a=15) and (d=4), what will be the (9)th term of the arithmetic progression?
B. (47)
(a_9=15+8(4)=47)। (9)वें पद तक (8) समान अंतर जुड़ते हैं। / (a_9=15+8(4)=47). Up to the (9)th term, (8) common differences are added.
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In the arithmetic progression \(3,11,19,27,\ldots\), which term is (67)?
C. (9)वाँ(9)th
(3+(n-1)8=67) से (8(n-1)=64) और (n=9)। पद का स्थान निकालने के लिए दिए पद को \(a_n\) के बराबर रखें। / From (3+(n-1)8=67), (8(n-1)=64) and (n=9). To find the position, set the given term equal to \(a_n\).
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If \(a_n=4n+3\), what will be the first four terms?
A. (7,11,15,19)
(n=1,2,3,4) रखने पर (7,11,15,19) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें। / Putting (n=1,2,3,4) gives (7,11,15,19). When forming terms from a rule, start (n) from (1).
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In an arithmetic progression, \(a_1=17\) and \(a_6=47\). What is the common difference?
B. (6)
\(a_6=a_1+5d\), इसलिए (47=17+5d) और (d=6)। दो पदों के बीच अंतरालों की संख्या गिनें। / \(a_6=a_1+5d\), so (47=17+5d) and (d=6). Count the number of gaps between the two terms.
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What is the sum of the first (5) terms of the arithmetic progression \(7,15,23,31,\ldots\)?
C. (115)
पहले (5) पद (7,15,23,31,39) हैं और योग (115) है। कम पद हों तो पद लिखकर जोड़ना सरल है। / The first (5) terms are (7,15,23,31,39), and their sum is (115). For a small number of terms, listing and adding is simple.
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If \(a_n=55-5n\), what is the common difference of this arithmetic progression?
A. (-5)
रैखिक रूप में (n) का गुणांक (-5) है, इसलिए समान अंतर (-5) है। गुणांक का चिह्न जरूर देखें। / In the linear form, the coefficient of (n) is (-5), so the common difference is (-5). Always check the sign of the coefficient.
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C. (5)
\(a_4=21+3d=36\) से (3d=15) और (d=5)। चौथे पद तक तीन अंतर होते हैं। / From \(a_4=21+3d=36\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.
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What is the (10)th term of the arithmetic progression \(4,13,22,31,\ldots\)?
C. (85)
यहाँ (a=4) और (d=9), इसलिए (a_{10}=4+9(9)=85)। (10)वें पद तक (9) अंतर जुड़ते हैं। / Here (a=4) and (d=9), so (a_{10}=4+9(9)=85). Up to the (10)th term, (9) gaps are added.
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If \(a_2=18\) and (d=6), what is \(a_1\)?
B. (12)
\(a_2=a_1+d\), इसलिए \(a_1=18-6=12\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं। / \(a_2=a_1+d\), so \(a_1=18-6=12\). If the second term is given, move one common difference backward.
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What will be the (12)th term of the arithmetic progression \(60,54,48,42,\ldots\)?
A. (-6)
यहाँ (a=60) और (d=-6), इसलिए (a_{12}=60+11(-6)=-6)। घटती श्रेढ़ी में पद ऋणात्मक भी हो सकते हैं। / Here (a=60) and (d=-6), so (a_{12}=60+11(-6)=-6). In a decreasing progression, terms can become negative.
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Which arithmetic progression has first term (12) and common difference (-4)?
C. \(12,8,4,0,\ldots\)
पहला पद (12) है और हर बार (4) घट रहा है। इसलिए समान अंतर (-4) है। / The first term is (12), and (4) is subtracted each time. Therefore the common difference is (-4).
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If \(a_n=6n-1\), what is the first term?
A. (5)
पहले पद के लिए (n=1), इसलिए \(a_1=6-1=5\)। पहला पद निकालने में (n=1) रखें। / For the first term (n=1), so \(a_1=6-1=5\). Put (n=1) to find the first term.
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In the arithmetic progression \(18,25,32,39,\ldots\), which term is (74)?
C. (9)वाँ(9)th
(18+(n-1)7=74) से (7(n-1)=56) और (n=9)। पद की स्थिति के लिए रैखिक समीकरण हल करें। / From (18+(n-1)7=74), (7(n-1)=56) and (n=9). Solve the linear equation to find the position of a term.
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What is the sum of the first (4) terms of the arithmetic progression \(12,20,28,36,\ldots\)?
C. (96)
पहले (4) पदों का योग (12+20+28+36=96) है। कम पद हों तो सीधे जोड़ना आसान है। / The sum of the first (4) terms is (12+20+28+36=96). If there are few terms, direct addition is easy.
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If (a=34) and (d=-7), what will \(a_6\) be?
A. (-1)
(a_6=34+5(-7)=-1)। ऋणात्मक समान अंतर को सही चिह्न के साथ रखें। / (a_6=34+5(-7)=-1). Keep the negative common difference with the correct sign.
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What is the general term of the arithmetic progression \(9,17,25,33,\ldots\)?
A. \(a_n=8n+1\)
पहला पद (9) और (d=8) है इसलिए (a_n=9+(n-1)8=8n+1)। विकल्प को (n=1) रखकर भी जांच सकते हैं। / The first term is (9) and (d=8), so (a_n=9+(n-1)8=8n+1). You can also check an option by putting (n=1).
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If an arithmetic progression has \(a_4=25\) and \(a_8=49\), what is the common difference?
C. (6)
चौथे से आठवें पद तक (4) अंतर हैं और वृद्धि (24) है, इसलिए (d=6)। अंतरालों की संख्या सही गिनें। / From the fourth to the eighth term there are (4) gaps and the increase is (24), so (d=6). Count the number of gaps correctly.
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If \(a_n=8n+5\), what is \(a_2+a_5\)?
B. (62)
\(a_2=21\) और \(a_5=45\), इसलिए योग (66) है। दोनों पद अलग निकालकर जोड़ें। / \(a_2=21\) and \(a_5=45\), so the sum is (66). Find both terms separately and then add.
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In the arithmetic progression \(90,82,74,66,\ldots\), which term is (18)?
B. (10)वाँ(10)th
(90+(n-1)(-8)=18) से (8(n-1)=72) और (n=10)। घटती श्रेढ़ी में भी वही \(a_n\) सूत्र लगता है। / From (90+(n-1)(-8)=18), (8(n-1)=72) and (n=10). The same \(a_n\) formula works in a decreasing progression.
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B. (16)
\(a_6=a+5d\), इसलिए (41=a+25) और (a=16)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं। / \(a_6=a+5d\), so (41=a+25) and (a=16). To move backward from a given term, subtract common differences.
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What is the common difference of the arithmetic progression \(12,12,12,12,\ldots\)?
A. (0)
हर लगातार अंतर (12-12=0) है। स्थिर अनुक्रम भी समानांतर श्रेढ़ी होता है। / Every consecutive difference is (12-12=0). A constant sequence is also an arithmetic progression.
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If (a=7) and (d=3), what will be the sum of the first (6) terms?
C. (87)
पहले (6) पद (7,10,13,16,19,22) हैं और योग (87) है। छोटे (n) में पद लिखकर जोड़ना आसान है। / The first (6) terms are (7,10,13,16,19,22), and their sum is (87). For small (n), writing and adding terms is easy.
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What is the (n)th term of the arithmetic progression \(22,29,36,43,\ldots\)?
B. \(a_n=7n+15\)
पहला पद (22) और (d=7) है इसलिए (a_n=22+(n-1)7=7n+15)। सामान्य पद बनाते समय (n-1) का ध्यान रखें। / The first term is (22) and (d=7), so (a_n=22+(n-1)7=7n+15). Remember (n-1) while forming the general term.
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If an arithmetic progression has \(a_5=33\) and (d=4), what will be \(a_{10}\)?
C. (53)
\(a_5\) से \(a_{10}\) तक (5) अंतर हैं, इसलिए (a_{10}=33+5(4)=53)। पास के पद से आगे बढ़ना तेज तरीका है। / From \(a_5\) to \(a_{10}\), there are (5) gaps, so (a_{10}=33+5(4)=53). Moving forward from a nearby term is a quick method.
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Which option has the first four terms of the arithmetic progression with (a=20) and (d=-5)?
C. (20,15,10,5)
पहला पद (20) है और हर बार (5) घटाने पर (20,15,10,5) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं। / The first term is (20), and subtracting (5) each time gives (20,15,10,5). Form terms directly from the given (a) and (d).
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C. (6)
समानांतर श्रेढ़ी में (2(2x)=(x+1)+(3x-5)), इससे (x=6) मिलता है। बीच का पद दोनों ओर के पदों का औसत होता है। / In an arithmetic progression, (2(2x)=(x+1)+(3x-5)), which gives (x=6). The middle term is the average of the two surrounding terms.
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What is the first negative term of the arithmetic progression \(38,33,28,23,\ldots\)?
B. (9)वाँ(9)th
\(a_8=3\) और \(a_9=-2\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद जांचें। / \(a_8=3\) and \(a_9=-2\), so the first negative term is the (9)th. Check the first term that goes below zero.
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If \(a_n=17-3n\), what is the fourth term of this arithmetic progression?
B. (5)
(a_4=17-3(4)=5)। दिए नियम में सीधे (n=4) रखें। / (a_4=17-3(4)=5). Substitute (n=4) directly in the given rule.
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What is the average of the first (3) terms of the arithmetic progression \(10,18,26,34,\ldots\)?
B. (18)
पहले तीन पदों का औसत \(\frac{10+18+26}{3}=18\) है। समानांतर श्रेढ़ी में तीन क्रमिक पदों का औसत बीच वाला पद होता है। / The average of the first three terms is \(\frac{10+18+26}{3}=18\). In an arithmetic progression, the average of three consecutive terms is the middle term.
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If \(a_1=11\) and \(a_{10}=65\), what will be the common difference?
C. (6)
\(a_{10}=11+9d=65\) से (9d=54) और (d=6)। (10)वें पद तक (9) अंतर होते हैं। / From \(a_{10}=11+9d=65\), (9d=54) and (d=6). Up to the (10)th term, there are (9) gaps.
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What is the (14)th term of the arithmetic progression \(5,14,23,32,\ldots\)?
D. (122)
यहाँ (a=5) और (d=9), इसलिए (a_{14}=5+13(9)=122)। बड़े पद के लिए भी वही सूत्र लगाएं। / Here (a=5) and (d=9), so (a_{14}=5+13(9)=122). Use the same formula even for a larger term.
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Which arithmetic progression has common difference (8)?
A. \(8,16,24,32,\ldots\)
\(8,16,24,32,\ldots\) में हर बार (8) जुड़ता है। समान अंतर निकालने में लगातार दो पदों का अंतर देखें। / In \(8,16,24,32,\ldots\), (8) is added each time. To find the common difference, check the difference of two consecutive terms.
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If \(a_n=9n+4\), at which term will \(a_n=85\)?
C. (9)वाँ(9)th
(9n+4=85) से (9n=81) और (n=9)। पद का स्थान निकालने के लिए \(a_n\) को दिए मान के बराबर रखें। / From (9n+4=85), (9n=81) and (n=9). To find the position, set \(a_n\) equal to the given value.
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What is the sum of the first (5) terms of the arithmetic progression \(44,38,32,26,\ldots\)?
B. (160)
पहले (5) पद (44,38,32,26,20) हैं और योग (160) है। घटती श्रेढ़ी में भी पद क्रम से लिखकर जोड़ें। / The first (5) terms are (44,38,32,26,20), and their sum is (160). In a decreasing progression, also list the terms in order and add.
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If an arithmetic progression has \(a_7=58\) and (d=8), what is \(a_4\)?
B. (34)
\(a_7\) से \(a_4\) तक (3) अंतर पीछे जाना है, इसलिए (a_4=58-3(8)=34)। पीछे जाते समय समान अंतर घटाएं। / From \(a_7\) to \(a_4\), move back (3) gaps, so (a_4=58-3(8)=34). When moving backward, subtract the common difference.
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In the arithmetic progression \(35,28,21,14,\ldots\), which term is (0)?
C. (6)वाँ(6)th
(35+(n-1)(-7)=0) से (n=6) मिलता है। शून्य भी श्रेढ़ी का पद हो सकता है। / From (35+(n-1)(-7)=0), (n=6). Zero can also be a term of a progression.
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If (a=23) and (d=0), what will be the (15)th term?
C. (23)
(d=0) होने पर हर पद (23) ही रहेगा। स्थिर समानांतर श्रेढ़ी में सभी पद बराबर होते हैं। / When (d=0), every term remains (23). In a constant arithmetic progression, all terms are equal.
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In the arithmetic progression \(4,12,20,28,\ldots\), what is the value of \(a_{12}-a_6\)?
B. (48)
\(a_{12}\) और \(a_6\) के बीच (6) अंतर हैं और (d=8), इसलिए अंतर (48) है। पदों का अंतर पद-संख्या के अंतर पर निर्भर करता है। / There are (6) gaps between \(a_{12}\) and \(a_6\), and (d=8), so the difference is (48). Term difference depends on the difference of positions.
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Which option has the first four terms formed by \(a_n=16-2n\)?
A. (14,12,10,8)
(n=1,2,3,4) रखने पर (14,12,10,8) मिलते हैं। नियम से पद बनाते समय (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (14,12,10,8). When forming terms from a rule, start with (n=1).
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What is the sum of the first (6) terms of the arithmetic progression \(15,21,27,33,\ldots\)?
C. (180)
पहले (6) पद (15,21,27,33,39,45) हैं और योग (180) है। पद सही क्रम में लिखकर जोड़ें। / The first (6) terms are (15,21,27,33,39,45), and their sum is (180). Write the terms in correct order and add.
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If an arithmetic progression has \(a_3=14\) and \(a_9=50\), what is \(a_6\)?
C. (32)
\(a_3\) से \(a_9\) तक (6) अंतर में वृद्धि (36) है इसलिए (d=6), अतः (a_6=14+3(6)=32)। पहले समान अंतर निकालें। / From \(a_3\) to \(a_9\), the increase over (6) gaps is (36), so (d=6), hence (a_6=14+3(6)=32). Find the common difference first.
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In the arithmetic progression \(9,16,23,\ldots\), what are the next two terms?
B. (30,37)
समान अंतर (7) है इसलिए (23) के बाद (30) और (37) आएंगे। अगले पदों के लिए समान अंतर जोड़ते रहें। / The common difference is (7), so after (23) the next terms are (30) and (37). Keep adding the common difference for next terms.
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If (a=5) and (d=13), what will \(a_7-a_2\) be?
B. (65)
\(a_7\) और \(a_2\) के बीच (5) अंतर हैं इसलिए अंतर \(5\times13=65\) है। पदों के अंतर के लिए पद-संख्या का अंतर देखें। / There are (5) gaps between \(a_7\) and \(a_2\), so the difference is \(5\times13=65\). For term difference, look at the difference of positions.
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What is the general term of the arithmetic progression \(31,35,39,43,\ldots\)?
A. \(a_n=4n+27\)
पहला पद (31) और (d=4) है इसलिए (a_n=31+(n-1)4=4n+27)। विकल्प की जांच के लिए (n=1) रखें। / The first term is (31) and (d=4), so (a_n=31+(n-1)4=4n+27). Put (n=1) to check an option.
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In the arithmetic progression \(2,9,16,23,\ldots\), what is the value of \(a_8+a_3\)?
A. (67)
यहाँ (d=7), इसलिए \(a_8=51\) और \(a_3=16\), योग (67) है। दोनों पद अलग निकालकर जोड़ें। / Here (d=7), so \(a_8=51\) and \(a_3=16\), and the sum is (67). Find both terms separately and then add.
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If an arithmetic progression has \(a_4=19\) and \(a_7=31\), what is \(a_1\)?
B. (7)
तीन अंतरों में वृद्धि (12) है इसलिए (d=4), फिर (a_1=19-3(4)=7)। बीच के पदों से पहले समान अंतर निकालें। / The increase over three gaps is (12), so (d=4), then (a_1=19-3(4)=7). From middle terms first find the common difference.
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Which arithmetic progression has \(a_5=30\) and common difference (6)?
A. \(6,12,18,24,\ldots\)
\(6,12,18,24,30,\ldots\) में पाँचवाँ पद (30) और समान अंतर (6) है। विकल्प में पहले पाँच पदों तक जांच करें। / In \(6,12,18,24,30,\ldots\), the fifth term is (30) and the common difference is (6). Check each option up to the fifth term.
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