Level 63 • 7/50 questions • 30 seconds per question.
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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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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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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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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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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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In which option do the terms form an arithmetic progression with common difference (0)?
A. (6, 6, 6, 6)
सभी पद समान हों तो हर अंतर (0) होता है। स्थिर क्रम भी समांतर श्रेणी होता है। / When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.
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A. (8) और (8)(8) and (8)
हर लगातार अंतर (8) है और (x) कट जाता है। समान चर वाले पदों में स्थिर भाग का अंतर देखें। / Every consecutive difference is (8), and (x) cancels out. For terms with the same variable part, compare the constant parts.
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