Level 50 • 50/50 questions • 35 seconds per question.
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What is the common difference in the sequence \(5,9,13,17,\ldots\)?
B. (4)
लगातार पदों का अंतर (9-5=4) है। समान अंतर निकालने के लिए दूसरे पद से पहला पद घटाएं। / The difference between consecutive terms is (9-5=4). To find the common difference, subtract the first term from the second term.
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If an arithmetic progression has first term (7) and common difference (3), what is the fifth term?
C. (19)
(a_5=7+(5-1)3=19)। (n)वें पद के लिए (a_n=a+(n-1)d) लगाएं। / (a_5=7+(5-1)3=19). Use (a_n=a+(n-1)d) for the (n)th term.
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Is the sequence \(20,16,12,8,\ldots\) an arithmetic progression?
A. हाँ क्योंकि समान अंतर (-4) हैYes because the common difference is (-4)
हर बार (4) घट रहा है इसलिए समान अंतर (-4) है। घटती हुई श्रेढ़ी भी समानांतर श्रेढ़ी हो सकती है। / Each time (4) is subtracted, so the common difference is (-4). A decreasing sequence can also be an arithmetic progression.
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What is the (10)th term of the arithmetic progression \(3,8,13,18,\ldots\)?
D. (48)
यहाँ (a=3) और (d=5), इसलिए (a_{10}=3+9(5)=48)। पद-संख्या से (1) कम अंतर जोड़े जाते हैं। / Here (a=3) and (d=5), so (a_{10}=3+9(5)=48). One less than the term number gives the number of differences added.
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If (a=11) and (d=-2), what will be the fourth term of the arithmetic progression?
C. (5)
(a_4=11+3(-2)=5)। ऋणात्मक समान अंतर को सूत्र में सही चिह्न के साथ रखें। / (a_4=11+3(-2)=5). Put the negative common difference in the formula with the correct sign.
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In the arithmetic progression \(6,10,14,18,\ldots\), which term is (38)?
A. (9)वाँ(9)th
(a_n=6+(n-1)4) और (6+4(n-1)=38) से (n=9)। पद का स्थान पूछे तो दिए पद को \(a_n\) के बराबर रखें। / (a_n=6+(n-1)4), and (6+4(n-1)=38) gives (n=9). When position is asked, set the given term equal to \(a_n\).
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Which option is an arithmetic progression?
B. \(1,5,9,13,\ldots\)
\(1,5,9,13,\ldots\) में समान अंतर (4) है। समानांतर श्रेढ़ी में लगातार अंतर बराबर होते हैं। / In \(1,5,9,13,\ldots\), the common difference is (4). In an arithmetic progression, consecutive differences are equal.
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In an arithmetic progression, \(a_1=4\) and \(a_6=24\). What is the common difference?
D. (4)
\(a_6=a_1+5d\), इसलिए (24=4+5d) और (d=4)। दो पदों के बीच अंतरों की संख्या गिनें। / \(a_6=a_1+5d\), so (24=4+5d) and (d=4). Count the number of gaps between the two terms.
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If the (n)th term of an arithmetic progression is \(a_n=2n+5\), what is the common difference?
C. (2)
रैखिक रूप \(a_n=2n+5\) में (n) का गुणांक (2) है। समानांतर श्रेढ़ी में यह गुणांक समान अंतर होता है। / In the linear form \(a_n=2n+5\), the coefficient of (n) is (2). In an arithmetic progression, this coefficient is the common difference.
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What is the (7)th term of the arithmetic progression \(15,12,9,6,\ldots\)?
A. (-3)
यहाँ (a=15) और (d=-3), इसलिए (a_7=15+6(-3)=-3)। घटती श्रेढ़ी में पद शून्य से नीचे भी जा सकते हैं। / Here (a=15) and (d=-3), so (a_7=15+6(-3)=-3). In a decreasing progression, terms may go below zero.
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What is the sum of the first (5) terms of the arithmetic progression \(2,7,12,17,\ldots\)?
B. (60)
पहले (5) पद (2,7,12,17,22) हैं और योग (60) है। छोटे (n) में पद लिखकर जोड़ना तेज होता है। / The first (5) terms are (2,7,12,17,22), and their sum is (60). For small (n), writing and adding terms is quick.
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If an arithmetic progression has (a=9) and (d=6), what will be the third term?
D. (21)
(a_3=9+2(6)=21)। तीसरे पद तक दो समान अंतर जोड़े जाते हैं। / (a_3=9+2(6)=21). Up to the third term, two common differences are added.
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What is the (n)th term of the arithmetic progression \(8,14,20,26,\ldots\)?
A. \(a_n=6n+2\)
पहला पद (8) और अंतर (6) है इसलिए (a_n=8+(n-1)6=6n+2)। सामान्य पद में (d) का गुणांक (n) के साथ आता है। / The first term is (8) and the difference is (6), so (a_n=8+(n-1)6=6n+2). In the general term, (d) appears with (n).
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C. (5)
\(a_4=12+3d=27\) से (3d=15) और (d=5)। चौथे पद तक तीन अंतर होते हैं। / From \(a_4=12+3d=27\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.
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Which arithmetic progression has first term (4) and common difference (7)?
B. \(4,11,18,25,\ldots\)
पहला पद (4) है और हर बार (7) जोड़ने पर \(4,11,18,25,\ldots\) मिलता है। पहले पद और अंतर दोनों मिलाने चाहिए। / The first term is (4), and adding (7) each time gives \(4,11,18,25,\ldots\). Both the first term and the difference must match.
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What is the sum of the first (6) terms of the arithmetic progression \(4,9,14,19,\ldots\)?
A. (99)
पहले (6) पद (4,9,14,19,24,29) हैं और उनका योग (99) है। छोटे पदों में सूची बनाकर जोड़ सकते हैं। / The first (6) terms are (4,9,14,19,24,29), and their sum is (99). For small terms, listing and adding works well.
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If \(a_n=30-4n\), what is the first term of this arithmetic progression?
B. (26)
पहले पद के लिए (n=1), इसलिए \(a_1=30-4=26\)। अनुक्रम में पहला पद निकालते समय (n=0) नहीं रखते। / For the first term (n=1), so \(a_1=30-4=26\). Do not use (n=0) when finding the first term of a sequence.
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What will be the (12)th term of the arithmetic progression \(1,6,11,16,\ldots\)?
C. (56)
यहाँ (a=1) और (d=5), इसलिए (a_{12}=1+11(5)=56)। (12)वें पद तक (11) अंतर जुड़ते हैं। / Here (a=1) and (d=5), so (a_{12}=1+11(5)=56). Up to the (12)th term, (11) differences are added.
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If an arithmetic progression has \(a_2=13\) and (d=4), what is \(a_1\)?
D. (9)
\(a_2=a_1+d\), इसलिए \(a_1=13-4=9\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं। / \(a_2=a_1+d\), so \(a_1=13-4=9\). If the second term is given, move one common difference backward.
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Which sequence is not an arithmetic progression?
C. \(3,6,12,24,\ldots\)
\(3,6,12,24,\ldots\) में अंतर (3,6,12) हैं, जो बराबर नहीं हैं। समानांतर श्रेढ़ी के लिए अंतर हमेशा समान होना चाहिए। / In \(3,6,12,24,\ldots\), the differences are (3,6,12), which are not equal. For an arithmetic progression, the difference must always be constant.
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In the arithmetic progression \(40,35,30,25,\ldots\), which term is (5)?
C. (8)वाँ(8)th
(a_n=40+(n-1)(-5)) और (40-5(n-1)=5) से (n=8)। घटती श्रेढ़ी में भी पद-संख्या धनात्मक होती है। / (a_n=40+(n-1)(-5)), and (40-5(n-1)=5) gives (n=8). In a decreasing progression, the position is still positive.
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B. (5)
\(a_7=3+6d=33\) से (6d=30) और (d=5)। सातवें पद तक छह अंतर होते हैं। / From \(a_7=3+6d=33\), (6d=30) and (d=5). Up to the seventh term, there are six gaps.
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What is the (n)th term of the arithmetic progression \(12,17,22,27,\ldots\)?
A. \(a_n=5n+7\)
यहाँ (a=12) और (d=5), इसलिए (a_n=12+(n-1)5=5n+7)। सामान्य पद बनाते समय (n-1) का उपयोग करें। / Here (a=12) and (d=5), so (a_n=12+(n-1)5=5n+7). Use (n-1) while forming the general term.
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If \(a_n=4n-1\), what is the (8)th term of this arithmetic progression?
C. (31)
(a_8=4(8)-1=31)। दिए हुए (n)वें पद में सीधे (n=8) रखें। / (a_8=4(8)-1=31). Substitute (n=8) directly in the given (n)th term.
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What is the sum of the first (4) terms of the arithmetic progression \(7,10,13,16,\ldots\)?
C. (46)
पहले (4) पदों का योग (7+10+13+16=46) है। कम पद हों तो सीधे जोड़ना सरल है। / The sum of the first (4) terms is (7+10+13+16=46). If there are few terms, direct addition is simple.
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Which arithmetic progression has common difference (-6)?
A. \(18,12,6,0,\ldots\)
\(18,12,6,0,\ldots\) में हर बार (6) घट रहा है, इसलिए (d=-6)। समान अंतर में चिह्न बहुत महत्वपूर्ण है। / In \(18,12,6,0,\ldots\), (6) is subtracted each time, so (d=-6). The sign is very important in common difference.
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If an arithmetic progression has \(a_4=18\) and (d=3), what will be \(a_9\)?
D. (33)
\(a_9\) तक \(a_4\) से (5) अंतर आगे हैं, इसलिए (a_9=18+5(3)=33)। पास के पद से आगे बढ़ना तेज तरीका है। / From \(a_4\) to \(a_9\), there are (5) gaps, so (a_9=18+5(3)=33). Moving forward from a nearby term is a quick method.
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What is the (11)th term of the arithmetic progression \(100,90,80,70,\ldots\)?
A. (0)
यहाँ (a=100) और (d=-10), इसलिए (a_{11}=100+10(-10)=0)। (11)वें पद तक (10) अंतर लगते हैं। / Here (a=100) and (d=-10), so (a_{11}=100+10(-10)=0). Up to the (11)th term, (10) gaps are used.
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If \(a_n=9n+2\), what is the first term of the arithmetic progression?
B. (11)
पहले पद के लिए (n=1), इसलिए \(a_1=9+2=11\)। \(a_n\) में पहला पद निकालने के लिए (n=1) रखें। / For the first term (n=1), so \(a_1=9+2=11\). To find the first term from \(a_n\), put (n=1).
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Which option has the first four terms of the arithmetic progression with (a=5) and (d=2)?
A. (5,7,9,11)
पहला पद (5) है और हर बार (2) जोड़ने पर (5,7,9,11) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं। / The first term is (5), and adding (2) each time gives (5,7,9,11). Form terms directly from the given (a) and (d).
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In the arithmetic progression \(13,19,25,31,\ldots\), which term is (61)?
C. (9)वाँ(9)th
(13+(n-1)6=61) से (6(n-1)=48) और (n=9)। पद की स्थिति के लिए रैखिक समीकरण हल करें। / From (13+(n-1)6=61), (6(n-1)=48) and (n=9). Solve the linear equation to find the position of a term.
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C. (4)
तीसरे से पाँचवें पद तक (2) अंतर हैं और वृद्धि (8) है, इसलिए (d=4)। पदों के बीच अंतरालों की संख्या गिनें। / From the third to the fifth term there are (2) gaps and the increase is (8), so (d=4). Count the number of gaps between terms.
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What is the (n)th term of the arithmetic progression \(22,18,14,10,\ldots\)?
A. \(a_n=26-4n\)
पहला पद (22) और (d=-4) है इसलिए (a_n=22+(n-1)(-4)=26-4n)। घटते क्रम में (d) को ऋणात्मक रखें। / The first term is (22) and (d=-4), so (a_n=22+(n-1)(-4)=26-4n). Keep (d) negative in a decreasing sequence.
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What is the average of the first (3) terms of the arithmetic progression \(2,8,14,20,\ldots\)?
C. (8)
पहले तीन पदों का औसत \(\frac{2+8+14}{3}=8\) है। समानांतर श्रेढ़ी में तीन क्रमिक पदों का औसत बीच वाला पद होता है। / The average of the first three terms is \(\frac{2+8+14}{3}=8\). In an arithmetic progression, the average of three consecutive terms is the middle term.
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If an arithmetic progression has (a=6) and \(a_5=30\), what is (d)?
C. (6)
\(a_5=6+4d=30\) से (4d=24) और (d=6)। पाँचवें पद तक चार समान अंतर जुड़ते हैं। / From \(a_5=6+4d=30\), (4d=24) and (d=6). Up to the fifth term, four common differences are added.
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Which option is an arithmetic progression with (d=0)?
A. \(4,4,4,4,\ldots\)
सभी पद (4) हैं इसलिए हर अंतर (0) है। स्थिर अनुक्रम भी समानांतर श्रेढ़ी होता है। / All terms are (4), so every difference is (0). A constant sequence is also an arithmetic progression.
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What is the (6)th term of the arithmetic progression \(17,23,29,35,\ldots\)?
C. (47)
यहाँ (a=17) और (d=6), इसलिए (a_6=17+5(6)=47)। (6)वें पद तक पाँच अंतर जुड़ते हैं। / Here (a=17) and (d=6), so (a_6=17+5(6)=47). Up to the (6)th term, five gaps are added.
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If \(a_n=5n+3\), what is the value of \(a_2+a_4\)?
D. (36)
\(a_2=13\) और \(a_4=23\), इसलिए योग (36) है। जोड़ने से पहले दोनों पद अलग निकालें। / \(a_2=13\) and \(a_4=23\), so the sum is (36). Find both terms separately before adding.
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Which term of the arithmetic progression \(50,45,40,35,\ldots\) is (0)?
C. (11)वाँ(11)th
(50+(n-1)(-5)=0) से (n=11)। शून्य भी श्रेढ़ी का पद हो सकता है। / From (50+(n-1)(-5)=0), (n=11). Zero can also be a term of a progression.
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In an arithmetic progression, (a=2) and (d=9). What will be \(a_8\)?
D. (65)
(a_8=2+7(9)=65)। आठवें पद तक सात समान अंतर जोड़े जाते हैं। / (a_8=2+7(9)=65). Up to the eighth term, seven common differences are added.
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What is the sum of the first (5) terms of the arithmetic progression \(3,13,23,33,\ldots\)?
C. (115)
पहले (5) पद (3,13,23,33,43) हैं और योग (115) है। पदों को सही क्रम में लिखकर जोड़ें। / The first (5) terms are (3,13,23,33,43), and the sum is (115). Write the terms in correct order and add them.
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If \(a_1=25\) and (d=-5), what is \(a_6\)?
A. (0)
(a_6=25+5(-5)=0)। ऋणात्मक अंतर के साथ घटाव सही तरीके से करें। / (a_6=25+5(-5)=0). Handle subtraction correctly with a negative difference.
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Which arithmetic progression has (n)th term \(a_n=3n+8\)?
B. \(11,14,17,20,\ldots\)
(n=1,2,3,4) रखने पर (11,14,17,20) मिलते हैं। नियम से पहले कुछ पद बनाकर मिलाएं। / Putting (n=1,2,3,4) gives (11,14,17,20). Form the first few terms from the rule and match.
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In the arithmetic progression \(6,15,24,33,\ldots\), which term is (69)?
B. (8)वाँ(8)th
(6+(n-1)9=69) से (9(n-1)=63) और (n=8)। पद की स्थिति निकालते समय (n-1) को न भूलें। / From (6+(n-1)9=69), (9(n-1)=63) and (n=8). Do not forget (n-1) while finding the position.
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If an arithmetic progression has \(a_5=28\) and (d=4), what is \(a_2\)?
B. (16)
\(a_5\) से \(a_2\) तक तीन अंतर पीछे जाना है, इसलिए (a_2=28-3(4)=16)। पीछे जाते समय समान अंतर घटाएं। / From \(a_5\) to \(a_2\), move back three gaps, so (a_2=28-3(4)=16). When moving backward, subtract the common difference.
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What is the first negative term of the arithmetic progression \(11,8,5,2,\ldots\)?
C. (6)वाँ(6)th
पद \(11,8,5,2,-1,\ldots\) नहीं बल्कि (5)वाँ पद (-1) है। इसलिए पहला ऋणात्मक पद (5)वाँ है। / The terms are \(11,8,5,2,-1,\ldots\), so the first negative term is the (5)th. Check terms in order when crossing zero.
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D. (7)
समानांतर श्रेढ़ी में (2(x+3)=(x-2)+(2x-1)), इससे (x=9) मिलता है। बीच का पद दो बराबर हिस्सों में होता है। / In an arithmetic progression, (2(x+3)=(x-2)+(2x-1)), which gives (x=9). The middle term is the average of the two adjacent terms.
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What is the (20)th term of the arithmetic progression \(4,4,4,4,\ldots\)?
B. (4)
इस श्रेढ़ी में (d=0) है, इसलिए हर पद (4) है। स्थिर समानांतर श्रेढ़ी में सभी पद बराबर होते हैं। / In this progression (d=0), so every term is (4). In a constant arithmetic progression, all terms are equal.
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If \(a_n=18-2n\), what is the value of \(a_3+a_6\)?
B. (24)
\(a_3=12\) और \(a_6=6\), इसलिए योग (18) नहीं बल्कि (18) है। गणना में दोनों पद अलग-अलग निकालें। / \(a_3=12\) and \(a_6=6\), so the sum is (18). Calculate both terms separately.
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What is the general term of the arithmetic progression \(21,28,35,42,\ldots\)?
A. \(a_n=7n+14\)
पहला पद (21) और (d=7) है इसलिए (a_n=21+(n-1)7=7n+14)। विकल्प को (n=1) रखकर भी जांच सकते हैं। / The first term is (21) and (d=7), so (a_n=21+(n-1)7=7n+14). You can also check an option by putting (n=1).
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