Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 391-400 of 600 questions.
If \(a_n=9n-4\), what is \(a_8-a_3\)?
B. (45)
\(a_8=68\) और \(a_3=23\), इसलिए अंतर (45) है। घटाने से पहले दोनों पदों की अलग गणना करें। / \(a_8=68\) and \(a_3=23\), so the difference is (45). Calculate both terms separately before subtracting.
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Which is the correct rule for the sequence \(5,14,29,50,\ldots\)?
A. \(a_n=3n^2+2\)
\(3n^2+2\) से (5,14,29,50) मिलते हैं। विकल्पों को शुरुआती पदों से मिलाएं। / \(3n^2+2\) gives (5,14,29,50). Match the options with the initial terms.
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If \(a_n=n^2+cn\) and \(a_3=18\), what is the value of (c)?
C. (3)
(9+3c=18) से (3c=9) और (c=3)। अज्ञात स्थिरांक के लिए दिया पद रखें। / From (9+3c=18), (3c=9) and (c=3). Substitute the given term to find the unknown constant.
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If \(a_n=12-2n\), which will be the first negative term?
B. (7)वाँ(7)th
\(a_6=0\) और \(a_7=-2\) है, इसलिए पहला ऋणात्मक पद (7)वाँ है। शून्य को ऋणात्मक न मानें। / \(a_6=0\) and \(a_7=-2\), so the first negative term is the (7)th. Do not count zero as negative.
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In an arithmetic sequence, \(a_3=13\) and \(a_6=25\). What is the value of \(a_9\)?
D. (37)
तीन अंतरों में वृद्धि (12) है इसलिए (d=4), अतः (a_9=25+3(4)=37)। समान अंतर को आगे बढ़ाकर पद निकालें। / The increase over three gaps is (12), so (d=4), hence (a_9=25+3(4)=37). Extend the terms using the common difference.
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What is the general term of the sequence \(2,9,28,65,\ldots\)?
A. \(a_n=n^3+1\)
यह \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\) है इसलिए \(a_n=n^3+1\)। घन अनुक्रम में स्थिर वृद्धि को पहचानें। / This is \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\), so \(a_n=n^3+1\). In cube sequences identify the constant shift.
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If (a_n=\frac{n(n+1)}{2}), at which term will \(a_n=45\)?
C. (9)वाँ(9)th
(n=9) रखने पर \(\frac{9\cdot10}{2}=45\) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है। / Putting (n=9) gives \(\frac{9\cdot10}{2}=45\). Direct option checking is a quick method.
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What is the general term of the sequence \(6,-9,12,-15,\ldots\)?
C. (a_n=(-1)^{n+1}3(n+1))
परिमाण \(6,9,12,15,\ldots\) है और चिह्न बदलता है इसलिए (a_n=(-1)^{n+1}3(n+1))। पहले पद के चिह्न से ((-1)) की शक्ति तय करें। / The magnitude is \(6,9,12,15,\ldots\) and signs alternate, so (a_n=(-1)^{n+1}3(n+1)). Use the first term sign to decide the power of ((-1)).
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A. \(a_n=5n-2\)
(a_1=18-3(5)=3) इसलिए (a_n=3+(n-1)5=5n-2)। दिए हुए बीच के पद से पहले पहला पद निकालें। / (a_1=18-3(5)=3), so (a_n=3+(n-1)5=5n-2). From a middle term first find the first term.
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If \(a_n=2n^2+n-1\), what is the value of \(a_6-a_2\)?
B. (68)
\(a_6=77\) और \(a_2=9\), इसलिए अंतर (68) है। घटाने से पहले दोनों पद अलग-अलग निकालें। / \(a_6=77\) and \(a_2=9\), so the difference is (68). Find both terms separately before subtracting.
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