Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the common difference in the sequence \(5,9,13,17,\ldots\)?
B. (4)
लगातार पदों का अंतर (9-5=4) है। समान अंतर निकालने के लिए दूसरे पद से पहला पद घटाएं। / The difference between consecutive terms is (9-5=4). To find the common difference, subtract the first term from the second term.
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If an arithmetic progression has first term (7) and common difference (3), what is the fifth term?
C. (19)
(a_5=7+(5-1)3=19)। (n)वें पद के लिए (a_n=a+(n-1)d) लगाएं। / (a_5=7+(5-1)3=19). Use (a_n=a+(n-1)d) for the (n)th term.
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Is the sequence \(20,16,12,8,\ldots\) an arithmetic progression?
A. हाँ क्योंकि समान अंतर (-4) हैYes because the common difference is (-4)
हर बार (4) घट रहा है इसलिए समान अंतर (-4) है। घटती हुई श्रेढ़ी भी समानांतर श्रेढ़ी हो सकती है। / Each time (4) is subtracted, so the common difference is (-4). A decreasing sequence can also be an arithmetic progression.
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What is the (10)th term of the arithmetic progression \(3,8,13,18,\ldots\)?
D. (48)
यहाँ (a=3) और (d=5), इसलिए (a_{10}=3+9(5)=48)। पद-संख्या से (1) कम अंतर जोड़े जाते हैं। / Here (a=3) and (d=5), so (a_{10}=3+9(5)=48). One less than the term number gives the number of differences added.
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If (a=11) and (d=-2), what will be the fourth term of the arithmetic progression?
C. (5)
(a_4=11+3(-2)=5)। ऋणात्मक समान अंतर को सूत्र में सही चिह्न के साथ रखें। / (a_4=11+3(-2)=5). Put the negative common difference in the formula with the correct sign.
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In the arithmetic progression \(6,10,14,18,\ldots\), which term is (38)?
A. (9)वाँ(9)th
(a_n=6+(n-1)4) और (6+4(n-1)=38) से (n=9)। पद का स्थान पूछे तो दिए पद को \(a_n\) के बराबर रखें। / (a_n=6+(n-1)4), and (6+4(n-1)=38) gives (n=9). When position is asked, set the given term equal to \(a_n\).
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Which option is an arithmetic progression?
B. \(1,5,9,13,\ldots\)
\(1,5,9,13,\ldots\) में समान अंतर (4) है। समानांतर श्रेढ़ी में लगातार अंतर बराबर होते हैं। / In \(1,5,9,13,\ldots\), the common difference is (4). In an arithmetic progression, consecutive differences are equal.
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In an arithmetic progression, \(a_1=4\) and \(a_6=24\). What is the common difference?
D. (4)
\(a_6=a_1+5d\), इसलिए (24=4+5d) और (d=4)। दो पदों के बीच अंतरों की संख्या गिनें। / \(a_6=a_1+5d\), so (24=4+5d) and (d=4). Count the number of gaps between the two terms.
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If the (n)th term of an arithmetic progression is \(a_n=2n+5\), what is the common difference?
C. (2)
रैखिक रूप \(a_n=2n+5\) में (n) का गुणांक (2) है। समानांतर श्रेढ़ी में यह गुणांक समान अंतर होता है। / In the linear form \(a_n=2n+5\), the coefficient of (n) is (2). In an arithmetic progression, this coefficient is the common difference.
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What is the (7)th term of the arithmetic progression \(15,12,9,6,\ldots\)?
A. (-3)
यहाँ (a=15) और (d=-3), इसलिए (a_7=15+6(-3)=-3)। घटती श्रेढ़ी में पद शून्य से नीचे भी जा सकते हैं। / Here (a=15) and (d=-3), so (a_7=15+6(-3)=-3). In a decreasing progression, terms may go below zero.
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