Level 61 • 22/50 questions • 40 seconds per question.
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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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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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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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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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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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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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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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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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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 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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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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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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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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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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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 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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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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In an arithmetic progression, when (d>0), how do the terms generally change?
B. बढ़ते हैंThey increase
धनात्मक (d) का अर्थ हर बार कुछ जोड़ना है। इसलिए पद बढ़ते हैं। / Positive (d) means something is added each time. Therefore, the terms increase.
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In an arithmetic progression, when (d<0), how do the terms generally change?
C. घटते हैंThey decrease
ऋणात्मक (d) का अर्थ हर बार घटाना है। इसलिए पद घटते हैं। / Negative (d) means subtraction occurs each time. Therefore, the terms decrease.
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In the sequence \(7,10,13,16,\ldots\), which term is (10)?
B. दूसरा पदSecond term
लिखे क्रम में (7) पहला और (10) दूसरा पद है। पद संख्या निकालते समय शुरुआत से गिनें। / In the written order, (7) is the first term and (10) is the second term. Count from the beginning to find the term position.
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If (a=4) and the next term is (9), what is (d)?
B. (5)
सार्व अंतर (9-4=5) है। अगले पद से पहले पद को घटाकर (d) निकालें। / The common difference is (9-4=5). Find (d) by subtracting the first term from the next term.
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