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 381-390 of 601 questions.
If \(a_1=4\) and (a_{n+1}=a_n+\frac{n(n+3)}{2}), what is \(a_5\)?
C. (34)
जुड़ने वाले मान (2,5,9,14) हैं इसलिए \(a_5=34\) है। भिन्न वाले जोड़ को पहले सरल करें। / The added values are (2,5,9,14), so \(a_5=34\). Exam tip: simplify the fractional increment first.
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If \(a_1=90\) and (a_{n+1}=a_n-\frac{n(n+3)}{2}), what is \(a_4\)?
C. (74)
घटने वाले मान (2,5,9) हैं इसलिए \(a_4=74\) है। भिन्न को सरल करके घटाएँ। / The subtracted values are (2,5,9), so \(a_4=74\). Exam tip: simplify the fraction before subtracting.
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If \(a_1=6\) and \(a_{n+1}=a_n+\frac{a_n}{2}+n\), what is \(a_3\)?
B. (17)
\(a_2=6+3+1=10\) और \(a_3=10+5+2=17\) है। पिछले पद का आधा लेकर (n) जोड़ें। / \(a_2=6+3+1=10\) and \(a_3=10+5+2=17\). Exam tip: take half of the previous term and add (n).
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If \(a_1=4\) and \(a_{n+1}=a_n+\frac{a_n}{4}+n\), what is \(a_3\)?
B. \(\frac{19}{2}\)
\(a_2=4+1+1=6\) और \(a_3=6+\frac{6}{4}+2=\frac{19}{2}\) है। भिन्नों को अंत तक ठीक रखें। / \(a_2=4+1+1=6\) and \(a_3=6+\frac{6}{4}+2=\frac{19}{2}\). Exam tip: keep fractions exact until the end.
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If \(a_1=2\) and \(a_{n+1}=a_n^2+n\), what is \(a_3\)?
C. (27)
\(a_2=2^2+1=5\) और \(a_3=5^2+2=27\) है। पिछले पद का वर्ग लेकर वर्तमान (n) जोड़ें। / \(a_2=2^2+1=5\) and \(a_3=5^2+2=27\). Exam tip: square the previous term and add the current (n).
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If \(a_1=3\) and \(a_{n+1}=a_n^2-n\), what is \(a_3\)?
C. (62)
\(a_2=3^2-1=8\) और \(a_3=8^2-2=62\) है। वर्ग निकालकर (n) घटाएँ। / \(a_2=3^2-1=8\) and \(a_3=8^2-2=62\). Exam tip: square first and then subtract (n).
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If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_4\)?
C. (20)
\(a_3=3+2\times2+3=10\) और \(a_4=10+2\times3+4=20\) है। वर्तमान (n) भी जोड़ना न भूलें। / \(a_3=3+2\times2+3=10\) and \(a_4=10+2\times3+4=20\). Exam tip: do not forget to add the current (n).
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If \(a_1=3\), \(a_2=4\), and \(a_n=3a_{n-1}-a_{n-2}+n\), what is \(a_4\)?
C. (36)
\(a_3=3\times4-3+3=12\) और \(a_4=3\times12-4+4=36\) है। दोनों पिछले पदों और वर्तमान (n) का उपयोग करें। / \(a_3=3\times4-3+3=12\) and \(a_4=3\times12-4+4=36\). Exam tip: use both previous terms and current (n).
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If \(a_1=5\) and (a_{n+1}=2a_n+(-1)^n), what is \(a_4\)?
C. (37)
पद (5,9,19,37) हैं इसलिए \(a_4=37\) है। ((-1)^n) का चिह्न हर चरण में जाँचें। / The terms are (5,9,19,37), so \(a_4=37\). Exam tip: check the sign of ((-1)^n) at each step.
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If \(a_1=30\) and (a_{n+1}=a_n-(-1)^n(2n+1)), what is \(a_4\)?
C. (35)
पद (30,33,28,35) हैं इसलिए \(a_4=35\) है। ऋण चिह्न और ((-1)^n) को साथ में देखें। / The terms are (30,33,28,35), so \(a_4=35\). Exam tip: track the minus sign and ((-1)^n) together.
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