Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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D. (12)
समानांतर श्रेढ़ी में (2(x+6)=x+2x), इसलिए (x=12)। बीच का पद दोनों ओर के पदों का औसत होता है। / In an arithmetic progression (2(x+6)=x+2x), so (x=12). The middle term is the average of the two surrounding terms.
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What is the first negative term of the arithmetic progression \(45,39,33,27,\ldots\)?
B. (9)वाँ(9)th
\(a_8=3\) और \(a_9=-3\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद जांचें। / \(a_8=3\) and \(a_9=-3\), so the first negative term is the (9)th. Check the first term that goes below zero.
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If \(a_n=11-2n\), what is the third term of this arithmetic progression?
B. (5)
(a_3=11-2(3)=5)। दिए नियम में सीधे (n=3) रखें। / (a_3=11-2(3)=5). Substitute (n=3) directly in the given rule.
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What is the average of the first (3) terms of the arithmetic progression \(6,14,22,30,\ldots\)?
B. (14)
पहले तीन पदों का औसत \(\frac{6+14+22}{3}=14\) है। समानांतर श्रेढ़ी में तीन क्रमिक पदों का औसत बीच वाला पद होता है। / The average of the first three terms is \(\frac{6+14+22}{3}=14\). In an arithmetic progression the average of three consecutive terms is the middle term.
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If \(a_1=5\) and \(a_{10}=50\), what will be the common difference?
B. (5)
\(a_{10}=5+9d=50\) से (9d=45) और (d=5)। (10)वें पद तक (9) अंतर होते हैं। / From \(a_{10}=5+9d=50\), (9d=45) and (d=5). Up to the (10)th term there are (9) gaps.
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What is the (15)th term of the arithmetic progression \(2,10,18,26,\ldots\)?
C. (114)
यहाँ (a=2) और (d=8), इसलिए (a_{15}=2+14(8)=114)। बड़े पद के लिए भी वही सूत्र लगाएं। / Here (a=2) and (d=8), so (a_{15}=2+14(8)=114). Use the same formula even for a larger term.
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Which arithmetic progression has common difference (9)?
A. \(9,18,27,36,\ldots\)
\(9,18,27,36,\ldots\) में हर बार (9) जुड़ता है। समान अंतर निकालने में लगातार दो पदों का अंतर देखें। / In \(9,18,27,36,\ldots\), (9) is added each time. To find the common difference check the difference of two consecutive terms.
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If \(a_n=6n+1\), at which term will \(a_n=49\)?
C. (8)वाँ(8)th
(6n+1=49) से (6n=48) और (n=8)। पद का स्थान निकालने के लिए \(a_n\) को दिए मान के बराबर रखें। / From (6n+1=49), (6n=48) and (n=8). To find the position set \(a_n\) equal to the given value.
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What is the sum of the first (5) terms of the arithmetic progression \(30,25,20,15,\ldots\)?
B. (100)
पहले (5) पद (30,25,20,15,10) हैं और योग (100) है। घटती श्रेढ़ी में भी पद क्रम से लिखकर जोड़ें। / The first (5) terms are (30,25,20,15,10), and their sum is (100). In a decreasing progression also list the terms in order and add.
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If an arithmetic progression has \(a_6=41\) and (d=7), what is \(a_3\)?
B. (20)
\(a_6\) से \(a_3\) तक (3) अंतर पीछे जाना है, इसलिए (a_3=41-3(7)=20)। पीछे जाते समय समान अंतर घटाएं। / From \(a_6\) to \(a_3\), move back (3) gaps, so (a_3=41-3(7)=20). When moving backward subtract the common difference.
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