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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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What is the sum of the first (5) terms of the arithmetic progression \(2,7,12,17,\ldots\)?
B. (60)
पहले (5) पद (2,7,12,17,22) हैं और योग (60) है। छोटे (n) में पद लिखकर जोड़ना तेज होता है। / The first (5) terms are (2,7,12,17,22), and their sum is (60). For small (n), writing and adding terms is quick.
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C. (5)
\(a_4=12+3d=27\) से (3d=15) और (d=5)। चौथे पद तक तीन अंतर होते हैं। / From \(a_4=12+3d=27\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.
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Which arithmetic progression has first term (4) and common difference (7)?
B. \(4,11,18,25,\ldots\)
पहला पद (4) है और हर बार (7) जोड़ने पर \(4,11,18,25,\ldots\) मिलता है। पहले पद और अंतर दोनों मिलाने चाहिए। / The first term is (4), and adding (7) each time gives \(4,11,18,25,\ldots\). Both the first term and the difference must match.
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What is the sum of the first (6) terms of the arithmetic progression \(4,9,14,19,\ldots\)?
A. (99)
पहले (6) पद (4,9,14,19,24,29) हैं और उनका योग (99) है। छोटे पदों में सूची बनाकर जोड़ सकते हैं। / The first (6) terms are (4,9,14,19,24,29), and their sum is (99). For small terms, listing and adding works well.
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If \(a_n=30-4n\), what is the first term of this arithmetic progression?
B. (26)
पहले पद के लिए (n=1), इसलिए \(a_1=30-4=26\)। अनुक्रम में पहला पद निकालते समय (n=0) नहीं रखते। / For the first term (n=1), so \(a_1=30-4=26\). Do not use (n=0) when finding the first term of a sequence.
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If an arithmetic progression has \(a_2=13\) and (d=4), what is \(a_1\)?
D. (9)
\(a_2=a_1+d\), इसलिए \(a_1=13-4=9\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं। / \(a_2=a_1+d\), so \(a_1=13-4=9\). If the second term is given, move one common difference backward.
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B. (5)
\(a_7=3+6d=33\) से (6d=30) और (d=5)। सातवें पद तक छह अंतर होते हैं। / From \(a_7=3+6d=33\), (6d=30) and (d=5). Up to the seventh term, there are six gaps.
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What is the sum of the first (4) terms of the arithmetic progression \(7,10,13,16,\ldots\)?
C. (46)
पहले (4) पदों का योग (7+10+13+16=46) है। कम पद हों तो सीधे जोड़ना सरल है। / The sum of the first (4) terms is (7+10+13+16=46). If there are few terms, direct addition is simple.
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If \(a_n=9n+2\), what is the first term of the arithmetic progression?
B. (11)
पहले पद के लिए (n=1), इसलिए \(a_1=9+2=11\)। \(a_n\) में पहला पद निकालने के लिए (n=1) रखें। / For the first term (n=1), so \(a_1=9+2=11\). To find the first term from \(a_n\), put (n=1).
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Which option has the first four terms of the arithmetic progression with (a=5) and (d=2)?
A. (5,7,9,11)
पहला पद (5) है और हर बार (2) जोड़ने पर (5,7,9,11) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं। / The first term is (5), and adding (2) each time gives (5,7,9,11). Form terms directly from the given (a) and (d).
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What is the average of the first (3) terms of the arithmetic progression \(2,8,14,20,\ldots\)?
C. (8)
पहले तीन पदों का औसत \(\frac{2+8+14}{3}=8\) है। समानांतर श्रेढ़ी में तीन क्रमिक पदों का औसत बीच वाला पद होता है। / The average of the first three terms is \(\frac{2+8+14}{3}=8\). In an arithmetic progression, the average of three consecutive terms is the middle term.
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If \(a_n=5n+3\), what is the value of \(a_2+a_4\)?
D. (36)
\(a_2=13\) और \(a_4=23\), इसलिए योग (36) है। जोड़ने से पहले दोनों पद अलग निकालें। / \(a_2=13\) and \(a_4=23\), so the sum is (36). Find both terms separately before adding.
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What is the sum of the first (5) terms of the arithmetic progression \(3,13,23,33,\ldots\)?
C. (115)
पहले (5) पद (3,13,23,33,43) हैं और योग (115) है। पदों को सही क्रम में लिखकर जोड़ें। / The first (5) terms are (3,13,23,33,43), and the sum is (115). Write the terms in correct order and add them.
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What is the first negative term of the arithmetic progression \(11,8,5,2,\ldots\)?
C. (6)वाँ(6)th
पद \(11,8,5,2,-1,\ldots\) नहीं बल्कि (5)वाँ पद (-1) है। इसलिए पहला ऋणात्मक पद (5)वाँ है। / The terms are \(11,8,5,2,-1,\ldots\), so the first negative term is the (5)th. Check terms in order when crossing zero.
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If \(a_n=18-2n\), what is the value of \(a_3+a_6\)?
B. (24)
\(a_3=12\) और \(a_6=6\), इसलिए योग (18) नहीं बल्कि (18) है। गणना में दोनों पद अलग-अलग निकालें। / \(a_3=12\) and \(a_6=6\), so the sum is (18). Calculate both terms separately.
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