Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 521-530 of 600 questions.
If \(a_n=pn+7\) and \(a_8=71\), what is the value of (p)?
C. (8)
(8p+7=71) से (8p=64) और (p=8)। अज्ञात गुणांक निकालने के लिए दिया पद नियम में रखें। / From (8p+7=71), (8p=64) and (p=8). Substitute the given term in the rule to find the unknown coefficient.
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If \(a_1=17\) and each next term is (9) less than the previous term, what is the explicit rule?
B. \(a_n=26-9n\)
पहला पद (17) और अंतर (-9) है इसलिए (a_n=17+(n-1)(-9)=26-9n)। घटने को ऋणात्मक अंतर मानें। / The first term is (17) and the difference is (-9), so (a_n=17+(n-1)(-9)=26-9n). Treat decrease as a negative difference.
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Which rule represents the sequence \(3,9,18,30,\ldots\)?
A. (a_n=\frac{3n(n+1)}{2})
यह (3) गुना त्रिभुज संख्याओं का क्रम है इसलिए (a_n=\frac{3n(n+1)}{2})। लगातार जोड़ (6,9,12) से पैटर्न पहचानें। / This is three times the triangular numbers, so (a_n=\frac{3n(n+1)}{2}). Recognize the pattern from additions (6,9,12).
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Which is the correct rule for the sequence \(12,25,42,63,\ldots\)?
A. \(a_n=2n^2+7n+3\)
\(2n^2+7n+3\) से (12,25,42,63) मिलते हैं। दूसरे अंतर स्थिर हों तो द्विघात नियम बनता है। / \(2n^2+7n+3\) gives (12,25,42,63). If second differences are constant, a quadratic rule fits.
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If \(a_n=\frac{3n}{n+4}\), at which term will \(a_n=\frac{9}{7}\)?
C. (6)वाँ(6)th
\(\frac{3n}{n+4}=\frac{9}{7}\) से (21n=9n+36) और (n=3) नहीं बल्कि (n=3) मिलता है। दिए विकल्पों में कोई सही नहीं है। / From \(\frac{3n}{n+4}=\frac{9}{7}\), (21n=9n+36), so (n=3). None of the given options is correct.
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If \(a_n=4n^2+3\), what is the value of \(a_3+a_5\)?
C. (142)
\(a_3=39\) और \(a_5=103\), इसलिए योग (142) है। जोड़ने से पहले दोनों पद अलग-अलग निकालें। / \(a_3=39\) and \(a_5=103\), so the sum is (142). Find both terms separately before adding.
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What is the general term of the sequence \(16,64,144,256,\ldots\)?
D. \(a_n=16n^2\)
यह \(4^2,8^2,12^2,16^2,\ldots\) है इसलिए (a_n=(4n)2=16n-2)। सम अंतर वाले वर्गों में आधार का नियम देखें। / This is \(4^2,8^2,12^2,16^2,\ldots\), so (a_n=(4n)2=16n-2). In square sequences with equal base gaps, find the base rule.
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Which is the correct rule for the sequence \(5,12,23,38,\ldots\)?
A. \(a_n=2n^2+n+2\)
\(2n^2+n+2\) से (5,12,23,38) मिलते हैं। बढ़ते अंतर (7,11,15) द्विघात नियम का संकेत देते हैं। / \(2n^2+n+2\) gives (5,12,23,38). Increasing differences (7,11,15) indicate a quadratic rule.
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If \(a_n=2^n+3n\), what will be the first four terms?
A. (5,10,17,28)
(n=1,2,3,4) रखने पर (5,10,17,28) मिलते हैं। घात और रैखिक भाग दोनों जोड़ना न भूलें। / Putting (n=1,2,3,4) gives (5,10,17,28). Do not forget to add both the power part and the linear part.
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What is the general term of the sequence \(6,-11,16,-21,\ldots\)?
B. (a_n=(-1)^{n+1}(5n+1))
परिमाण \(6,11,16,21,\ldots\) है और चिह्न धन से शुरू होकर बदलता है इसलिए (a_n=(-1)^{n+1}(5n+1))। पहले पद का चिह्न शक्ति तय करता है। / The magnitude is \(6,11,16,21,\ldots\) and signs start positive and alternate, so (a_n=(-1)^{n+1}(5n+1)). The sign of the first term decides the power.
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