Topic Quiz • 150 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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What is the common difference in the sequence \(14,20,26,32,\ldots\)?
B. (6)
लगातार पदों का अंतर (20-14=6) है। समान अंतर निकालने के लिए दूसरे पद से पहला पद घटाएं। / The difference between consecutive terms is (20-14=6). To find the common difference subtract the first term from the second term.
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If an arithmetic progression has first term (9) and common difference (4), what is the (8)th term?
C. (37)
(a_8=9+(8-1)4=37)। (n)वें पद के लिए (a_n=a+(n-1)d) का प्रयोग करें। / (a_8=9+(8-1)4=37). 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 \(35,31,27,23,\ldots\)?
B. \(a_n=39-4n\)
पहला पद (35) और अंतर (-4) है इसलिए (a_n=35+(n-1)(-4)=39-4n)। घटती श्रेढ़ी में समान अंतर ऋणात्मक होता है। / The first term is (35) and the difference is (-4), so (a_n=35+(n-1)(-4)=39-4n). In a decreasing progression the common difference is negative.
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Why is the sequence \(2,5,9,14,\ldots\) not an arithmetic progression?
A. क्योंकि अंतर (3,4,5) बराबर नहीं हैंBecause the differences (3,4,5) are not equal
लगातार अंतर (3,4,5) हैं जो समान नहीं हैं। समानांतर श्रेढ़ी में हर बार समान अंतर होना चाहिए। / The consecutive differences are (3,4,5), which are not equal. An arithmetic progression must have the same difference each time.
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If (a=6) and (d=7), what will be the (5)th term of the arithmetic progression?
B. (34)
(a_5=6+(5-1)7=34)। पाँचवें पद तक चार समान अंतर जुड़ते हैं। / (a_5=6+(5-1)7=34). Up to the fifth term four common differences are added.
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In the arithmetic progression \(8,13,18,23,\ldots\), which term is (48)?
C. (9)वाँ(9)th
(8+(n-1)5=48) से (n=9) मिलता है। पद का स्थान निकालने के लिए दिए पद को \(a_n\) के बराबर रखें। / From (8+(n-1)5=48), (n=9). To find the position set the given term equal to \(a_n\).
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If \(a_n=3n+2\), what will be the first four terms?
A. (5,8,11,14)
(n=1,2,3,4) रखने पर (5,8,11,14) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें। / Putting (n=1,2,3,4) gives (5,8,11,14). When forming terms from a rule start (n) from (1).
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In an arithmetic progression \(a_1=12\) and \(a_6=32\). What is the common difference?
B. (4)
\(a_6=a_1+5d\) इसलिए (32=12+5d) और (d=4)। दो पदों के बीच अंतरालों की संख्या गिनें। / \(a_6=a_1+5d\), so (32=12+5d) and (d=4). 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 \(5,12,19,26,\ldots\)?
C. (95)
पहले (5) पद (5,12,19,26,33) हैं और योग (95) है। कम पद हों तो सीधे लिखकर जोड़ना सरल है। / The first (5) terms are (5,12,19,26,33), and their sum is (95). For a small number of terms direct listing and addition is simple.
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If \(a_n=42-6n\), what is the common difference of this arithmetic progression?
A. (-6)
रैखिक रूप में (n) का गुणांक (-6) है इसलिए समान अंतर (-6) है। गुणांक का चिह्न जरूर देखें। / In the linear form the coefficient of (n) is (-6), so the common difference is (-6). Always check the sign of the coefficient.
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Which sequence is an arithmetic progression?
C. \(7,11,15,19,\ldots\)
\(7,11,15,19,\ldots\) में समान अंतर (4) है। समानांतर श्रेढ़ी में लगातार अंतर बराबर होते हैं। / In \(7,11,15,19,\ldots\), the common difference is (4). In an arithmetic progression consecutive differences are equal.
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C. (4)
\(a_4=18+3d=30\) से (3d=12) और (d=4)। चौथे पद तक तीन अंतर होते हैं। / From \(a_4=18+3d=30\), (3d=12) and (d=4). Up to the fourth term there are three gaps.
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What is the (12)th term of the arithmetic progression \(11,17,23,29,\ldots\)?
C. (77)
यहाँ (a=11) और (d=6), इसलिए (a_{12}=11+11(6)=77)। (12)वें पद तक (11) अंतर जुड़ते हैं। / Here (a=11) and (d=6), so (a_{12}=11+11(6)=77). Up to the (12)th term (11) gaps are added.
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If \(a_2=15\) and (d=5), what is \(a_1\)?
B. (10)
\(a_2=a_1+d\) इसलिए \(a_1=15-5=10\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं। / \(a_2=a_1+d\), so \(a_1=15-5=10\). If the second term is given move one common difference backward.
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What will be the (9)th term of the arithmetic progression \(28,24,20,16,\ldots\)?
A. (-4)
यहाँ (a=28) और (d=-4), इसलिए (a_9=28+8(-4)=-4)। घटती श्रेढ़ी में पद ऋणात्मक भी हो सकते हैं। / Here (a=28) and (d=-4), so (a_9=28+8(-4)=-4). In a decreasing progression terms can become negative.
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Which arithmetic progression has first term (6) and common difference (-3)?
C. \(6,3,0,-3,\ldots\)
पहला पद (6) है और हर बार (3) घट रहा है। इसलिए समान अंतर (-3) है। / The first term is (6), and (3) is subtracted each time. Therefore the common difference is (-3).
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If \(a_n=7n-2\), what is the first term?
A. (5)
पहले पद के लिए (n=1), इसलिए \(a_1=7-2=5\)। पहला पद निकालने में (n=1) रखें। / For the first term (n=1), so \(a_1=7-2=5\). Put (n=1) to find the first term.
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In the arithmetic progression \(16,21,26,31,\ldots\), which term is (56)?
C. (9)वाँ(9)th
(16+(n-1)5=56) से (n=9) मिलता है। पद की स्थिति के लिए सरल रैखिक समीकरण हल करें। / From (16+(n-1)5=56), (n=9). Solve the simple 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 \(9,15,21,27,\ldots\)?
B. (72)
पहले (4) पदों का योग (9+15+21+27=72) है। कम पद हों तो सीधे जोड़ना आसान है। / The sum of the first (4) terms is (9+15+21+27=72). If there are few terms direct addition is easy.
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If (a=25) and (d=-5), what will \(a_7\) be?
B. (-5)
(a_7=25+6(-5)=-5)। ऋणात्मक समान अंतर को सही चिह्न के साथ रखें। / (a_7=25+6(-5)=-5). Keep the negative common difference with the correct sign.
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What is the general term of the arithmetic progression \(4,11,18,25,\ldots\)?
A. \(a_n=7n-3\)
पहला पद (4) और (d=7) है इसलिए (a_n=4+(n-1)7=7n-3)। विकल्प को (n=1) रखकर भी जांच सकते हैं। / The first term is (4) and (d=7), so (a_n=4+(n-1)7=7n-3). You can also check an option by putting (n=1).
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If an arithmetic progression has \(a_3=19\) and \(a_6=34\), what is the common difference?
C. (5)
तीसरे से छठे पद तक (3) अंतर हैं और वृद्धि (15) है, इसलिए (d=5)। अंतरालों की संख्या सही गिनें। / From the third to the sixth term there are (3) gaps and the increase is (15), so (d=5). Count the number of gaps correctly.
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If \(a_n=5n+6\), what is \(a_3+a_5\)?
D. (52)
\(a_3=21\) और \(a_5=31\), इसलिए योग (52) है। जोड़ने से पहले दोनों पद अलग निकालें। / \(a_3=21\) and \(a_5=31\), so the sum is (52). Find both terms separately before adding.
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In the arithmetic progression \(70,62,54,46,\ldots\), which term is (14)?
B. (8)वाँ(8)th
(70+(n-1)(-8)=14) से (n=8) मिलता है। घटती श्रेढ़ी में भी वही \(a_n\) सूत्र लगता है। / From (70+(n-1)(-8)=14), (n=8). The same \(a_n\) formula works in a decreasing progression.
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B. (15)
\(a_5=a+4d\) इसलिए (27=a+12) और (a=15)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं। / \(a_5=a+4d\), so (27=a+12) and (a=15). To move backward from a given term subtract common differences.
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What is the common difference of the arithmetic progression \(3,3,3,3,\ldots\)?
A. (0)
हर लगातार अंतर (3-3=0) है। स्थिर अनुक्रम भी समानांतर श्रेढ़ी होता है। / Every consecutive difference is (3-3=0). A constant sequence is also an arithmetic progression.
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If (a=10) and (d=2), what will be the sum of the first (6) terms?
C. (90)
पहले (6) पद (10,12,14,16,18,20) हैं और योग (90) है। छोटे (n) में पद लिखकर जोड़ना आसान है। / The first (6) terms are (10,12,14,16,18,20), and their sum is (90). For small (n), writing and adding terms is easy.
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What is the (n)th term of the arithmetic progression \(19,23,27,31,\ldots\)?
B. \(a_n=4n+15\)
पहला पद (19) और (d=4) है इसलिए (a_n=19+(n-1)4=4n+15)। सामान्य पद बनाते समय (n-1) का ध्यान रखें। / The first term is (19) and (d=4), so (a_n=19+(n-1)4=4n+15). Remember (n-1) while forming the general term.
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If an arithmetic progression has \(a_4=22\) and (d=6), what will be \(a_9\)?
D. (52)
\(a_4\) से \(a_9\) तक (5) अंतर हैं, इसलिए (a_9=22+5(6)=52)। पास के पद से आगे बढ़ना तेज तरीका है। / From \(a_4\) to \(a_9\), there are (5) gaps, so (a_9=22+5(6)=52). 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=13) and (d=5)?
A. (13,18,23,28)
पहला पद (13) है और हर बार (5) जोड़ने पर (13,18,23,28) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं। / The first term is (13), and adding (5) each time gives (13,18,23,28). Form the terms directly from the given (a) and (d).
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D. (12)
समानांतर श्रेढ़ी में (2(x+6)=x+2x), इसलिए (x=12)। बीच का पद दोनों ओर के पदों का औसत होता है। / In an arithmetic progression (2(x+6)=x+2x), so (x=12). 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 \(45,39,33,27,\ldots\)?
B. (9)वाँ(9)th
\(a_8=3\) और \(a_9=-3\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद जांचें। / \(a_8=3\) and \(a_9=-3\), so the first negative term is the (9)th. Check the first term that goes below zero.
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If \(a_n=11-2n\), what is the third term of this arithmetic progression?
B. (5)
(a_3=11-2(3)=5)। दिए नियम में सीधे (n=3) रखें। / (a_3=11-2(3)=5). Substitute (n=3) directly in the given rule.
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What is the average of the first (3) terms of the arithmetic progression \(6,14,22,30,\ldots\)?
B. (14)
पहले तीन पदों का औसत \(\frac{6+14+22}{3}=14\) है। समानांतर श्रेढ़ी में तीन क्रमिक पदों का औसत बीच वाला पद होता है। / The average of the first three terms is \(\frac{6+14+22}{3}=14\). In an arithmetic progression the average of three consecutive terms is the middle term.
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If \(a_1=5\) and \(a_{10}=50\), what will be the common difference?
B. (5)
\(a_{10}=5+9d=50\) से (9d=45) और (d=5)। (10)वें पद तक (9) अंतर होते हैं। / From \(a_{10}=5+9d=50\), (9d=45) and (d=5). Up to the (10)th term there are (9) gaps.
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What is the (15)th term of the arithmetic progression \(2,10,18,26,\ldots\)?
C. (114)
यहाँ (a=2) और (d=8), इसलिए (a_{15}=2+14(8)=114)। बड़े पद के लिए भी वही सूत्र लगाएं। / Here (a=2) and (d=8), so (a_{15}=2+14(8)=114). Use the same formula even for a larger term.
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Which arithmetic progression has common difference (9)?
A. \(9,18,27,36,\ldots\)
\(9,18,27,36,\ldots\) में हर बार (9) जुड़ता है। समान अंतर निकालने में लगातार दो पदों का अंतर देखें। / In \(9,18,27,36,\ldots\), (9) is added each time. To find the common difference check the difference of two consecutive terms.
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If \(a_n=6n+1\), at which term will \(a_n=49\)?
C. (8)वाँ(8)th
(6n+1=49) से (6n=48) और (n=8)। पद का स्थान निकालने के लिए \(a_n\) को दिए मान के बराबर रखें। / From (6n+1=49), (6n=48) and (n=8). 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 \(30,25,20,15,\ldots\)?
B. (100)
पहले (5) पद (30,25,20,15,10) हैं और योग (100) है। घटती श्रेढ़ी में भी पद क्रम से लिखकर जोड़ें। / The first (5) terms are (30,25,20,15,10), and their sum is (100). In a decreasing progression also list the terms in order and add.
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If an arithmetic progression has \(a_6=41\) and (d=7), what is \(a_3\)?
B. (20)
\(a_6\) से \(a_3\) तक (3) अंतर पीछे जाना है, इसलिए (a_3=41-3(7)=20)। पीछे जाते समय समान अंतर घटाएं। / From \(a_6\) to \(a_3\), move back (3) gaps, so (a_3=41-3(7)=20). When moving backward subtract the common difference.
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In the arithmetic progression \(24,18,12,6,\ldots\), which term is (0)?
B. (5)वाँ(5)th
(24+(n-1)(-6)=0) से (n=5) मिलता है। शून्य भी श्रेढ़ी का पद हो सकता है। / From (24+(n-1)(-6)=0), (n=5). Zero can also be a term of a progression.
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If (a=17) and (d=0), what will be the (10)th term?
C. (17)
(d=0) होने पर हर पद (17) ही रहेगा। स्थिर समानांतर श्रेढ़ी में सभी पद बराबर होते हैं। / When (d=0), every term remains (17). In a constant arithmetic progression all terms are equal.
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In the arithmetic progression \(1,7,13,19,\ldots\), what is the value of \(a_{11}-a_5\)?
C. (36)
\(a_{11}\) और \(a_5\) के बीच (6) अंतर हैं और (d=6), इसलिए अंतर (36) है। समानांतर श्रेढ़ी में पदों का अंतर पद-संख्या के अंतर पर निर्भर करता है। / There are (6) gaps between \(a_{11}\) and \(a_5\), and (d=6), so the difference is (36). In an arithmetic progression term difference depends on the difference of positions.
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Which option has the first four terms formed by \(a_n=10-3n\)?
A. (7,4,1,-2)
(n=1,2,3,4) रखने पर (7,4,1,-2) मिलते हैं। नियम से पद बनाते समय (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (7,4,1,-2). 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 \(10,16,22,28,\ldots\)?
C. (150)
पहले (6) पद (10,16,22,28,34,40) हैं और योग (150) है। पद सही क्रम में लिखकर जोड़ें। / The first (6) terms are (10,16,22,28,34,40), and their sum is (150). Write the terms in correct order and add.
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If an arithmetic progression has \(a_2=9\) and \(a_8=39\), what is \(a_5\)?
C. (24)
\(a_2\) से \(a_8\) तक (6) अंतर में वृद्धि (30) है इसलिए (d=5), अतः (a_5=9+3(5)=24)। पहले समान अंतर निकालें। / From \(a_2\) to \(a_8\), the increase over (6) gaps is (30), so (d=5), hence (a_5=9+3(5)=24). Find the common difference first.
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In the arithmetic progression \(6,10,14,\ldots\), what are the next two terms?
B. (18,22)
समान अंतर (4) है इसलिए (14) के बाद (18) और (22) आएंगे। अगले पदों के लिए समान अंतर जोड़ते रहें। / The common difference is (4), so after (14) the next terms are (18) and (22). Keep adding the common difference for next terms.
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If (a=3) and (d=11), what will \(a_6-a_2\) be?
B. (44)
\(a_6\) और \(a_2\) के बीच (4) अंतर हैं इसलिए अंतर \(4\times11=44\) है। पदों के अंतर के लिए पद-संख्या का अंतर देखें। / There are (4) gaps between \(a_6\) and \(a_2\), so the difference is \(4\times11=44\). For term difference look at the difference of positions.
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What is the general term of the arithmetic progression \(27,30,33,36,\ldots\)?
A. \(a_n=3n+24\)
पहला पद (27) और (d=3) है इसलिए (a_n=27+(n-1)3=3n+24)। विकल्प की जांच के लिए (n=1) रखें। / The first term is (27) and (d=3), so (a_n=27+(n-1)3=3n+24). Put (n=1) to check an option.
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What is the first negative term in the arithmetic progression \(32,27,22,17,\ldots\)?
B. (8)वाँ(8)th
\(a_7=2\) और \(a_8=-3\), इसलिए पहला ऋणात्मक पद (8)वाँ है। शून्य से नीचे जाने वाला पहला पद ध्यान से जांचें। / \(a_7=2\) and \(a_8=-3\), so the first negative term is the (8)th. Check carefully for the first term that goes below zero.
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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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