common-difference se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
216 questions tagged with common-difference.
If (a, b, c) are in an arithmetic progression, what is the value of (a-2b+c)?
B. (0)
समांतर श्रेणी में (2b=a+c). इसलिए (a-2b+c=0). / In an arithmetic progression, (2b=a+c). Therefore (a-2b+c=0).
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In the sequence \(101, 97, 93, 89, \ldots\), what is the common difference and what is its nature?
B. (-4), ऋणात्मक(-4), negative
हर अगला पद पिछले से (4) कम है, इसलिए (d=-4). घटती समांतर श्रेणी में सामान्य अंतर ऋणात्मक होता है। / Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.
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If (5-2t, 7-t, 12+t) are in an arithmetic progression, what is the value of (t)?
A. (-3)
अंतर (t+2) और (t+5) नहीं, सही दूसरा अंतर (5+2t) है। (t+2=5+2t) से (t=-3). / The differences are not (t+2) and (t+5); the correct second difference is (5+2t). From (t+2=5+2t), (t=-3).
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Which sequence has common difference \(\frac{3}{4}\)?
A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\)
पहले विकल्प में हर लगातार अंतर \(\frac{3}{4}\) है। भिन्नों में हर को समान बनाकर अंतर निकालना सुरक्षित तरीका है। / In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.
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If (1, 1+2p, 1+5p, 1+9p) is an arithmetic progression, what is correct about (p)?
A. (p=0)
अंतर (2p, 3p, 4p) हैं। ये बराबर केवल (p=0) पर होंगे। / The differences are (2p, 3p, 4p). They are equal only when (p=0).
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A. (0)
बराबर अंतर के लिए (-x+8=-2x+16), जिससे (x=8). तब दोनों अंतर (0) हैं। / For equal differences, (-x+8=-2x+16), which gives (x=8). Then both differences are (0).
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The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. What is the common difference?
A. (8)
अंतर (-x+8) और (-2x+16) हैं। बराबर करने पर (x=8), इसलिए (d=0) नहीं बल्कि (d=0) आता है। / The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).
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If (6, h, 30) are in an arithmetic progression, which pair of (h) and common difference is correct?
B. (h=18, d=12)
बीच का पद \(\frac{6+30}{2}=18\) है। सामान्य अंतर (18-6=12) है। / The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).
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For which (s) will \(\frac{s}{2}, s+3, 3s-1\) form an arithmetic progression?
C. (8)
पहला अंतर \(\frac{s}{2}+3\) और दूसरा अंतर (2s-4) है। बराबर करने पर (s=8) मिलता है। / The first difference is \(\frac{s}{2}+3\), and the second is (2s-4). Equating them gives (s=8).
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If (x, x+6, 3x-2) are in an arithmetic progression, what is the correct value of (x)?
C. (7)
अंतर (6) और (2x-8) बराबर होने चाहिए। इसलिए (2x-8=6) से (x=7). / The differences (6) and (2x-8) must be equal. Thus (2x-8=6), giving (x=7).
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If (x, x+6, 3x-2) are in an arithmetic progression, what is the third term?
B. (16)
(2(x+6)=x+(3x-2)) से (x=9). तीसरा पद (3x-2=25) नहीं, इसलिए विकल्पों में सही मान नहीं है। / From (2(x+6)=x+(3x-2)), (x=7). The third term is (3x-2=19), so none of the options is correct.
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A. (r=-2, d=1)
अंतर (r+3) और (2r+5) हैं। बराबर करने पर (r=-2) और (d=1) मिलता है। / The differences are (r+3) and (2r+5). Equating them gives (r=-2) and (d=1).
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If (2, 5, 10, 17) is called an arithmetic progression, what does the correct check show?
C. यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैंIt is not an arithmetic progression because the differences are (3,5,7)
समांतर श्रेणी के लिए हर लगातार अंतर समान होना चाहिए। यहाँ (3,5,7) समान नहीं हैं। / For an arithmetic progression, every consecutive difference must be equal. Here (3,5,7) are not equal.
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What mistake is made if (81, 27, 9, 3) is considered an arithmetic progression?
B. अनुपात समान है, अंतर समान नहींThe ratio is constant, not the difference
इस क्रम में अनुपात \(\frac{1}{3}\) है, पर अंतर (-54, -18, -6) बराबर नहीं हैं। समांतर श्रेणी में अनुपात नहीं, अंतर देखें। / This sequence has ratio \(\frac{1}{3}\), but differences (-54, -18, -6) are not equal. In an arithmetic progression, check difference, not ratio.
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If (3z, z+10, 22-z) are in an arithmetic progression, what is the first term?
C. (12)
(2(z+10)=3z+(22-z)) से (z=4). पहला पद (3z=12) है। / From (2(z+10)=3z+(22-z)), (z=4). The first term is (3z=12).
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For which (n) will (n+2, 2n+5, 4n+8) form an arithmetic progression?
A. (0)
लगातार अंतर (n+3) और (2n+3) हैं। बराबर करने पर (n=0) मिलता है। / The consecutive differences are (n+3) and (2n+3). Equating them gives (n=0).
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If (14, 14-d, 14-2d, 14-3d) is an arithmetic progression, what is the common difference?
B. (-d)
हर अगला पद पिछले पद से (d) कम है। इसलिए सामान्य अंतर (-d) है। / Each next term is (d) less than the previous term. Therefore the common difference is (-d).
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The sequence (2, 2+k, 2+4k, 2+9k) can be an arithmetic progression. Under what condition?
A. (k=0)
अंतर (k, 3k, 5k) हैं। ये सभी बराबर केवल (k=0) पर होंगे। / The differences are (k, 3k, 5k). They are all equal only when (k=0).
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If (u, v, w) are in an arithmetic progression and (u+w=48), what is the value of (v)?
D. (24)
तीन पदों वाली समांतर श्रेणी में (2v=u+w). इसलिए (v=24). / In a three-term arithmetic progression, (2v=u+w). Therefore (v=24).
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What is the correct conclusion about the sequence (9, y, 2y+6)?
C. यह किसी भी (y) पर समांतर श्रेणी नहीं हैIt is not an arithmetic progression for any (y)
समांतर श्रेणी के लिए (2y=9+(2y+6)) चाहिए, जिससे (0=15) असंभव है। असंभव समीकरण आने पर कोई मान नहीं होता। / For an arithmetic progression, (2y=9+(2y+6)) is required, which gives the impossible (0=15). When an impossible equation appears, no value works.
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If (9, y, 2y+6) are in an arithmetic progression, what is the common difference?
B. (15)
(2y=9+(2y+6)) से (0=15) नहीं, इसलिए यह कभी समांतर श्रेणी नहीं बनती। सही विकल्पों में ऐसा कोई सामान्य अंतर नहीं है। / From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.
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B. (0)
तीन पदों वाली समांतर श्रेणी में पहला और तीसरा पद मिलकर दूसरे पद का दोगुना देते हैं। यहाँ (2(a+d)=0). / In a three-term arithmetic progression, the first and third terms sum to twice the middle term. Here (2(a+d)=0).
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Which sequence has a negative common difference and all consecutive differences equal?
B. (20, 16, 12, 8)
(20,16,12,8) में हर बार (4) घटता है, इसलिए (d=-4). केवल घटते क्रम को देखकर नहीं, बराबर अंतर भी जांचें। / In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.
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If terms are formed by \(A_n=4n-9\), what does \(A_{15}-A_{14}\) represent?
B. सामान्य अंतरCommon difference
समांतर श्रेणी में लगातार दो पदों का अंतर सामान्य अंतर होता है। यहाँ \(A_{15}-A_{14}=4\). / In an arithmetic progression, the difference of two consecutive terms is the common difference. Here \(A_{15}-A_{14}=4\).
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For what value will the common differences of (2x+5, 4x+1, 7x-7) be equal?
C. (4)
पहला अंतर (2x-4) और दूसरा अंतर (3x-8) है। दोनों बराबर करने पर (x=4). / The first difference is (2x-4), and the second is (3x-8). Equating them gives (x=4).
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If (12, b, 2b-3, 39) are in an arithmetic progression, what is the value of (b)?
C. (21)
पहले से चौथे पद तक तीन समान अंतर हैं, इसलिए (d=9). दूसरा पद (12+9=21), अतः (b=21). / From the first to the fourth term, there are three equal gaps, so (d=9). The second term is (12+9=21), hence (b=21).
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Four numbers (x-6, x+1, 2x-1, 3x-8) are in an arithmetic progression. What is the common difference?
C. (7)
पहला अंतर हमेशा (7) है। (x-2=7) से (x=9) और अंतिम अंतर भी (7) हो जाता है। / The first difference is always (7). From (x-2=7), (x=9), and the last difference also becomes (7).
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If (5, 5+t, 5+3t, 5+6t) is an arithmetic progression, which value of (t) is possible?
A. (0)
अंतर (t, 2t, 3t) हैं और तीनों बराबर तभी होंगे जब (t=0). ऐसे प्रश्नों में सभी लगातार अंतर जांचें। / The differences are (t, 2t, 3t), and all are equal only when (t=0). In such questions, check every consecutive difference.
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A. (c=0)
लगातार अंतर (-c) और (-2c) हैं। बराबर होने के लिए (c=0) होना चाहिए। / The consecutive differences are (-c) and (-2c). They are equal only when (c=0).
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If (2a+3, 5a-1, 11a-13) are in an arithmetic progression, what is the second term?
C. (14)
(2(5a-1)=(2a+3)+(11a-13)) से (a=3). दूसरा पद (5a-1=14) है। / From (2(5a-1)=(2a+3)+(11a-13)), (a=3). The second term is (5a-1=14).
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