Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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If a sequence is \(1,4,7,10,\ldots\), what is the difference between the third and second terms?
B. (3)
तीसरा पद (7) और दूसरा पद (4) है। इसलिए अंतर (7-4=3) है। / The third term is (7) and the second term is (4). Therefore, the difference is (7-4=3).
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What is the common difference of the arithmetic progression \(a-2,a+1,a+4,a+7,\ldots\)?
B. (3)
लगातार पदों का अंतर ((a+1)-(a-2)=3) है। चर वाले पदों में समान पद कट जाते हैं। / The difference of consecutive terms is ((a+1)-(a-2)=3). Like terms cancel in variable terms.
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In which sequence are the consecutive differences not equal?
D. \(2,3,5,8,\ldots\)
\(2,3,5,8,\ldots\) में अंतर (1,2,3) हैं। इसलिए लगातार अंतर बराबर नहीं हैं। / In \(2,3,5,8,\ldots\), the differences are (1,2,3). Hence the consecutive differences are not equal.
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B. (7)
सार्व अंतर (18-11=7) है। (d) के लिए दूसरा पद घटा पहला पद करें। / The common difference is (18-11=7). For (d), subtract the first term from the second term.
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In the sequence \(25,21,17,13,\ldots\), which term is (21)?
B. दूसरा पदSecond term
लिखे क्रम में (25) पहला और (21) दूसरा पद है। पद की स्थिति के लिए क्रम से गिनें। / In the written order, (25) is the first term and (21) is the second term. Count in order to find the position.
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If (a=2.5) and (d=1.5), what are the first three terms?
A. (2.5,4.0,5.5)
पहला पद (2.5) है और हर बार (1.5) जोड़ना है। इसलिए पद (2.5,4.0,5.5) हैं। / The first term is (2.5), and (1.5) is added each time. Hence the terms are (2.5,4.0,5.5).
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What will be the sixth term in \(-18,-12,-6,0,\ldots\)?
B. (12)
यहाँ सार्व अंतर (6) है। पाँचवाँ पद (6) और छठा पद (12) होगा। / The common difference is (6). The fifth term is (6) and the sixth term is (12).
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If an arithmetic progression has (a=28) and second term (19), what is the common difference?
B. (-9)
सार्व अंतर (19-28=-9) है। दूसरे पद से पहले पद को घटाकर (d) निकालें। / The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
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What is the common difference of \(5m,5m-4,5m-8,5m-12,\ldots\)?
B. (-4)
लगातार पदों का अंतर ((5m-4)-5m=-4) है। बीजीय पदों में समान पद काटकर अंतर निकालें। / The difference of consecutive terms is ((5m-4)-5m=-4). In algebraic terms, cancel like terms to find the difference.
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In which sequence are the first three consecutive differences (4,4,4)?
A. \(2,6,10,14,\ldots\)
\(2,6,10,14,\ldots\) में अंतर (4,4,4) हैं। समान अंतर समांतर श्रेढ़ी की पहचान है। / In \(2,6,10,14,\ldots\), the differences are (4,4,4). Equal differences identify an arithmetic progression.
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