Level 61 • 21/50 questions • 35 seconds per question.
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In the sequence \(-2,3,8,13,\ldots\), what are (a) and (d) respectively?
A. (-2) और (5)(-2) and (5)
पहला पद (-2) है और (3-(-2)=5) है। ऋणात्मक पदों में घटाव सावधानी से करें। / The first term is (-2) and (3-(-2)=5). Be careful while subtracting negative terms.
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What is the common difference in the sequence \(5x,5x+2,5x+4,\ldots\)?
A. (2)
सार्व अंतर ((5x+2)-5x=2) है। बीजगणितीय पदों में भी दूसरे पद में से पहला पद घटाएं। / The common difference is ((5x+2)-5x=2). For algebraic terms also subtract the first term from the second.
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If \(p,11,15,19,\ldots\) is an arithmetic progression, what is the value of (p)?
C. (7)
(11,15,19) में सार्व अंतर (4) है इसलिए (p=11-4=7)। पहले पद के लिए पीछे की ओर (d) घटाएं। / The common difference in (11,15,19) is (4), so (p=11-4=7). For the first term move backward by subtracting (d).
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If (3,m,11) are three consecutive terms of an arithmetic progression, what is (m)?
A. (7)
बीच का पद (3) और (11) का औसत है इसलिए \(m=\frac{3+11}{2}=7\)। तीन क्रमागत पदों में मध्य पद औसत होता है। / The middle term is the average of (3) and (11), so \(m=\frac{3+11}{2}=7\). In three consecutive terms the middle term is the average.
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If (a=-5) and (d=4), what are the first four terms?
D. (-5,-1,3,7)
हर बार (4) जोड़ने पर (-5,-1,3,7) मिलते हैं। (d) को लगातार जोड़ना न भूलें। / Adding (4) each time gives (-5,-1,3,7). Do not forget to add (d) repeatedly.
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If two consecutive terms in an arithmetic progression are (12) and (17), what is (d)?
C. (5)
सार्व अंतर (17-12=5) है। लगातार पद दिए हों तो बाद वाला पद घटा पहले वाला पद करें। / The common difference is (17-12=5). When consecutive terms are given, subtract the earlier term from the later term.
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If (6,10,n,18) are consecutive terms of an arithmetic progression, what is (n)?
D. (14)
सार्व अंतर (10-6=4) है इसलिए (n=10+4=14)। पहले दो पदों से (d) निकालना आसान होता है। / The common difference is (10-6=4), so (n=10+4=14). It is easy to find (d) from the first two terms.
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Which option has (a=9) and (d=3)?
B. \(9,12,15,18,\ldots\)
\(9,12,15,18,\ldots\) में पहला पद (9) और अंतर (3) है। (a) और (d) दोनों शर्तें एक साथ जांचें। / In \(9,12,15,18,\ldots\), the first term is (9) and the difference is (3). Check both (a) and (d) together.
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What is the difference between the third and fourth terms of \(42,39,36,33,\ldots\)?
B. (-3)
तीसरा पद (36) और चौथा (33) है इसलिए (33-36=-3)। अंतर निकालते समय बाद वाला पद घटा पहले वाला पद करें। / The third term is (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from the next term.
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If (a=2.5) and (d=1.5), what is the second term?
C. (4.0)
दूसरा पद (a+d=2.5+1.5=4.0) है। दशमलव जोड़ते समय अंकों को ठीक से मिलाएं। / The second term is (a+d=2.5+1.5=4.0). Align digits carefully when adding decimals.
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B. (7)
((x+7)-x=7) है इसलिए अंतर (7) है। समान जोड़ी गई संख्या ही (d) होती है। / ((x+7)-x=7), so the difference is (7). The equal added number is (d).
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In an arithmetic progression, the first term is (13) and the second term is (8). What is (d)?
B. (-5)
(d=8-13=-5) है। दूसरा पद छोटा हो तो (d) ऋणात्मक होगा। / (d=8-13=-5). If the second term is smaller, (d) will be negative.
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Which of the following sequences has (a=-4) and (d=6)?
B. \(-4,2,8,14,\ldots\)
\(-4,2,8,14,\ldots\) में पहला पद (-4) और अंतर (6) है। दोनों शर्तें मिलनी चाहिए। / In \(-4,2,8,14,\ldots\), the first term is (-4) and the difference is (6). Both conditions must match.
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In which sequence are the terms decreasing by an equal amount but (d) is not (-2)?
A. \(20,17,14,11,\ldots\)
\(20,17,14,11,\ldots\) में (d=-3) है, (-2) नहीं। विकल्पों में चिह्न और मान दोनों जांचें। / In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
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If \(y-2,y+1,y+4,\ldots\) is an arithmetic progression, what is (d)?
B. (3)
(d=(y+1)-(y-2)=3) है। चर कट जाने पर स्थिर अंतर मिलता है। / (d=(y+1)-(y-2)=3). When variables cancel, the constant difference remains.
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If (a=12) and (d=-4), which is the correct order of the first three terms?
A. (12,8,4)
हर बार (-4) जोड़ने पर (12,8,4) मिलता है। ऋणात्मक अंतर को घटाव की तरह समझें। / Adding (-4) each time gives (12,8,4). Understand negative difference as subtraction.
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In the sequence \(0,-3,-6,-9,\ldots\), what are (a) and (d) respectively?
C. (0) और (-3)(0) and (-3)
पहला पद (0) है और (d=-3-0=-3) है। शून्य भी पहला पद हो सकता है। / The first term is (0), and (d=-3-0=-3). Zero can also be the first term.
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D. (30)
तीसरा पद (50) और पहला (20) है इसलिए अंतर (30) है। यह (2d) के बराबर है। / The third term is (50) and the first is (20), so the difference is (30). It equals (2d).
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If the first two terms of an arithmetic progression are (-7) and (-2), what will be the third term?
A. (3)
सार्व अंतर (-2-(-7)=5) है इसलिए तीसरा पद (-2+5=3) है। ऋणात्मक संख्याओं में चिह्न सावधानी से देखें। / The common difference is (-2-(-7)=5), so the third term is (-2+5=3). Watch signs carefully with negative numbers.
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If (9,b,21) are consecutive terms of an arithmetic progression, what is the value of (b)?
C. (15)
मध्य पद \(b=\frac{9+21}{2}=15\) है। तीन क्रमागत पदों में बीच वाला पद औसत होता है। / The middle term is \(b=\frac{9+21}{2}=15\). In three consecutive terms the middle term is the average.
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In an arithmetic progression, (d=4) and the second term is (11). What is the first term?
A. (7)
पहला पद (11-4=7) है। दूसरे पद से (d) घटाकर पहला पद मिलता है। / The first term is (11-4=7). Subtract (d) from the second term to get the first term.
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