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What is the common difference of AP 5, 8, 11, 14?
B. 3
सार्व अंतर = 8 - 5 = 3 है। प्रत्येक क्रमागत पद में 3 की वृद्धि हो रही है। / The common difference is 8 - 5 = 3. Each successive term increases by 3.
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What is the common difference in the sequence \(3,7,11,15,\ldots\)?
C. (4)
लगातार पदों का अंतर (7-3=4) है। परीक्षा में सार्व अंतर के लिए दूसरा पद घटा पहला पद करें। / The difference of consecutive terms is (7-3=4). In exams, find common difference by subtracting the first term from the second term.
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In an arithmetic progression, how is the common difference (d) found?
A. \(d=a_2-a_1\)
सार्व अंतर लगातार दो पदों का अंतर होता है। इसलिए \(d=a_2-a_1\) सही है। / The common difference is the difference between two consecutive terms. Hence \(d=a_2-a_1\) is correct.
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What is the common difference in \(10,8,6,4,\ldots\)?
B. (-2)
यहाँ (8-10=-2) है। घटती हुई समांतर श्रेढ़ी में सार्व अंतर ऋणात्मक हो सकता है। / Here (8-10=-2). In a decreasing arithmetic progression, the common difference can be negative.
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Which sequence is an arithmetic progression?
C. \(5,10,15,20,\ldots\)
\(5,10,15,20,\ldots\) में हर बार (5) जुड़ता है। समान अंतर वाली श्रेढ़ी समांतर श्रेढ़ी होती है। / In \(5,10,15,20,\ldots\), (5) is added each time. A sequence with equal differences is an arithmetic progression.
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What is the common difference of \(6,6,6,6,\ldots\)?
D. (0)
लगातार पदों का अंतर (6-6=0) है। समान पदों वाला अनुक्रम भी सार्व अंतर (0) के साथ समांतर श्रेढ़ी होता है। / The difference of consecutive terms is (6-6=0). A constant sequence is also an arithmetic progression with common difference (0).
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What is the first term of the arithmetic progression \(12,17,22,27,\ldots\)?
B. (12)
समांतर श्रेढ़ी का प्रथम पद पहला लिखा हुआ पद होता है। यहाँ प्रथम पद (12) है। / The first term of an arithmetic progression is the first written term. Here the first term is (12).
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In the sequence \(4,9,14,\Box,24,\ldots\), what is the value of \(\Box\)?
C. (19)
यहाँ सार्व अंतर (5) है। इसलिए (14+5=19) होगा। / The common difference is (5). Therefore, (14+5=19).
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Which sequence is not an arithmetic progression?
D. \(2,5,9,14,\ldots\)
\(2,5,9,14,\ldots\) में अंतर (3,4,5) हैं। अंतर समान न हो तो अनुक्रम समांतर श्रेढ़ी नहीं होता। / In \(2,5,9,14,\ldots\), the differences are (3,4,5). If differences are not equal, the sequence is not an arithmetic progression.
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A. (8)
दूसरा पद (a+d) होता है। इसलिए (5+3=8) है। / The second term is (a+d). Therefore, (5+3=8).
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