arithmetic-progression se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
221 questions tagged with arithmetic-progression.
In the sequence \(50,45,40,35,\ldots\), how much less is each term than the previous term?
C. (5)
हर अगला पद पिछले पद से (5) कम है। इसका सार्व अंतर (-5) होगा। / Each next term is (5) less than the previous term. Its common difference will be (-5).
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B. (2)
हर अगली पंक्ति में (2) सीटें बढ़ती हैं। इसलिए सार्व अंतर (2) है। / Each next row increases by (2) seats. Therefore, the common difference is (2).
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If a sequence is \(5,5,5,5,\ldots\), what type of arithmetic progression is it?
C. समान पदों वालीConstant terms
सभी पद समान हैं इसलिए (d=0) है। इसे समान पदों वाली समांतर श्रेढ़ी कह सकते हैं। / All terms are equal, so (d=0). It can be called an arithmetic progression with constant terms.
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Which term is not given in the arithmetic progression \(18,21,24,27,\ldots\)?
D. (30)
लिखे हुए पद (18,21,24,27) हैं। (30) अगला पद हो सकता है पर दिए गए पदों में नहीं है। / The written terms are (18,21,24,27). (30) can be the next term but is not among the given terms.
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What will be the next two terms in \(40,35,30,25,\ldots\)?
C. (20,15)
यहाँ सार्व अंतर (-5) है। इसलिए (25-5=20) और (20-5=15)। / The common difference is (-5). Therefore, (25-5=20) and (20-5=15).
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Which sequence starts with (a=9) and (d=2)?
A. \(9,11,13,15,\ldots\)
पहला पद (9) है और हर बार (2) जोड़ना है। इसलिए सही अनुक्रम \(9,11,13,15,\ldots\) है। / The first term is (9), and (2) is added each time. Hence the correct sequence is \(9,11,13,15,\ldots\).
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If (a=2) and (d=5), what are the first three terms?
B. (2,7,12)
पहला पद (2) है और हर बार (5) जोड़ना है। इसलिए पहले तीन पद (2,7,12) हैं। / The first term is (2), and (5) is added each time. Therefore, the first three terms are (2,7,12).
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C. (3)
हर अगला पद पिछले पद से (3) अधिक है। यही इस श्रेढ़ी का सार्व अंतर है। / Each next term is (3) greater than the previous term. This is the common difference of the sequence.
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Is the sequence \(4,8,13,19,\ldots\) an arithmetic progression or not?
C. नहीं क्योंकि अंतर समान नहीं हैंNo because differences are not equal
इसके अंतर (4,5,6) हैं। समान अंतर न होने से यह समांतर श्रेढ़ी नहीं है। / Its differences are (4,5,6). Since the differences are not equal, it is not an arithmetic progression.
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A. (5)
सार्व अंतर दूसरा पद घटा पहला पद होता है। इसलिए (23-18=5)। / The common difference is the second term minus the first term. Therefore, (23-18=5).
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What is the common difference of the arithmetic progression \(-10,-6,-2,2,\ldots\)?
B. (4)
यहाँ (-6-(-10)=4) है। ऋणात्मक संख्याओं के साथ घटाव सावधानी से करें। / Here (-6-(-10)=4). Subtract carefully when negative numbers are involved.
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Which sequence is an arithmetic progression because of equal differences?
B. \(3,8,13,18,\ldots\)
\(3,8,13,18,\ldots\) में अंतर हमेशा (5) है। इसलिए यह समांतर श्रेढ़ी है। / In \(3,8,13,18,\ldots\), the difference is always (5). Hence it is an arithmetic progression.
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What will be the fifth term in \(2,7,12,17,\ldots\)?
C. (22)
यहाँ सार्व अंतर (5) है। चौथे पद (17) में (5) जोड़ने पर पाँचवाँ पद (22) मिलता है। / The common difference is (5). Adding (5) to the fourth term (17) gives the fifth term (22).
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If (d=0), what will be the form of an arithmetic progression?
A. सभी पद समान होंगेAll terms will be equal
(d=0) का अर्थ है कि कोई बदलाव नहीं हो रहा। इसलिए सभी पद समान होंगे। / (d=0) means there is no change between terms. Therefore, all terms will be equal.
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In \(11,15,19,23,\ldots\), what are (d) and (a) respectively?
B. (d=4,\ a=11)
पहला पद (a=11) और सार्व अंतर (15-11=4) है। क्रमशः पूछे गए मानों का क्रम ध्यान रखें। / The first term is (a=11) and the common difference is (15-11=4). Keep the asked order of values in mind.
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What is the common difference of the arithmetic progression \(0,3,6,9,\ldots\)?
B. (3)
लगातार पदों का अंतर (3-0=3) है। पहला पद (0) हो सकता है फिर भी श्रेढ़ी समांतर हो सकती है। / The difference of consecutive terms is (3-0=3). The first term can be (0), and the sequence can still be an arithmetic progression.
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Which sequence has common difference (-4)?
B. \(20,16,12,8,\ldots\)
\(20,16,12,8,\ldots\) में हर बार (4) घटता है। इसलिए सार्व अंतर (-4) है। / In \(20,16,12,8,\ldots\), (4) is subtracted each time. Therefore, the common difference is (-4).
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What is the fourth term in \(14,18,22,26,\ldots\)?
C. (26)
चौथा पद सीधे (26) है। पद क्रम गिनते समय पहला पद (14) से शुरू करें। / The fourth term is directly (26). While counting positions, start from the first term (14).
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A. \(6,10,14,18,\ldots\)
पहले दिन (6) और हर दिन (4) अधिक है। इसलिए अनुक्रम \(6,10,14,18,\ldots\) होगा। / The first day has (6), and (4) more are planted each day. Hence the sequence is \(6,10,14,18,\ldots\).
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What is the common difference of \(100,90,80,70,\ldots\)?
B. (-10)
यहाँ (90-100=-10) है। घटते अनुक्रम में उत्तर को धनात्मक न मान लें। / Here (90-100=-10). Do not take the answer as positive in a decreasing sequence.
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If (a=9) and (d=-2), what is the second term of the arithmetic progression?
A. (7)
दूसरा पद (a+d=9+(-2)=7) है। ऋणात्मक अंतर जोड़ते समय चिन्ह सावधानी से लगाएँ। / The second term is (a+d=9+(-2)=7). Use signs carefully while adding a negative difference.
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Why is \(3,6,12,24,\ldots\) not an arithmetic progression?
C. क्योंकि लगातार अंतर समान नहीं हैंBecause consecutive differences are not equal
अंतर (3,6,12) हैं जो समान नहीं हैं। इसलिए यह समांतर श्रेढ़ी नहीं है। / The differences are (3,6,12), which are not equal. Hence it is not an arithmetic progression.
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Which option states the correct property of an arithmetic progression?
B. हर दो लगातार पदों का अंतर समान होता हैThe difference between every two consecutive terms is equal
समांतर श्रेढ़ी में लगातार पदों का अंतर स्थिर होता है। यही इसकी मुख्य पहचान है। / In an arithmetic progression, the difference between consecutive terms is constant. This is its main identity.
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Which is the third term in the arithmetic progression \(2,5,8,11,\ldots\)?
C. (8)
तीसरा लिखा हुआ पद (8) है। आसान प्रश्नों में पद की स्थिति ध्यान से गिनें। / The third written term is (8). In easy questions, count the position of the term carefully.
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What will be the next term in \(30,27,24,21,\ldots\)?
C. (18)
यहाँ सार्व अंतर (-3) है। इसलिए अगला पद (21-3=18) होगा। / The common difference is (-3). Therefore, the next term is (21-3=18).
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If the arithmetic progression is \(a,a+2,a+4,a+6,\ldots\), what is the common difference?
C. (2)
लगातार पदों का अंतर ((a+2)-a=2) है। अक्षर वाले पदों में भी घटाकर अंतर निकालें। / The difference of consecutive terms is ((a+2)-a=2). For algebraic terms also, subtract to find the difference.
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Which sequence is an arithmetic progression with (d=3)?
B. \(4,7,10,13,\ldots\)
\(4,7,10,13,\ldots\) में हर बार (3) जुड़ता है। इसलिए इसका सार्व अंतर (3) है। / In \(4,7,10,13,\ldots\), (3) is added each time. Hence its common difference is (3).
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What is the common difference of \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?
A. \(\frac{1}{2}\)
यहाँ \(1-\frac{1}{2}=\frac{1}{2}\) है। भिन्नों में भी सार्व अंतर लगातार पदों से ही निकलेगा। / Here \(1-\frac{1}{2}=\frac{1}{2}\). For fractions also, the common difference is found from consecutive terms.
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What is the common difference of \(1.5,2.0,2.5,3.0,\ldots\)?
B. (0.5)
लगातार पदों का अंतर (2.0-1.5=0.5) है। दशमलव पदों में भी समान अंतर जाँचना होता है। / The difference of consecutive terms is (2.0-1.5=0.5). Even for decimal terms, equal differences must be checked.
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If each next term of a sequence is (7) more than the previous term, what is its common difference?
C. (7)
हर बार (7) जोड़ने का अर्थ सार्व अंतर (7) है। ऐसी श्रेढ़ी समांतर श्रेढ़ी होगी। / Adding (7) each time means the common difference is (7). Such a sequence will be an arithmetic progression.
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