अनुक्रम \(5,9,13,17,\ldots\) में समान अंतर क्या है?
What is the common difference in the sequence \(5,9,13,17,\ldots\)?
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A (3)
B (4)
C (5)
D (9)
Explanation opens after your attempt
Step 1
Concept
The difference between consecutive terms is (9-5=4). To find the common difference, subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (4). The difference between consecutive terms is (9-5=4). To find the common difference, subtract the first term from the second term.
Step 3
Exam Tip
लगातार पदों का अंतर (9-5=4) है। समान अंतर निकालने के लिए दूसरे पद से पहला पद घटाएं।
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यदि किसी समानांतर श्रेढ़ी में पहला पद (7) और समान अंतर (3) है, तो पाँचवाँ पद क्या होगा?
If an arithmetic progression has first term (7) and common difference (3), what is the fifth term?
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A (16)
B (18)
C (19)
D (22)
Explanation opens after your attempt
Step 1
Concept
(a_5=7+(5-1)3=19). Use (a_n=a+(n-1)d) for the (n)th term.
Step 2
Why this answer is correct
The correct answer is C. (19). (a_5=7+(5-1)3=19). Use (a_n=a+(n-1)d) for the (n)th term.
Step 3
Exam Tip
(a_5=7+(5-1)3=19)। (n)वें पद के लिए (a_n=a+(n-1)d) लगाएं।
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अनुक्रम \(20,16,12,8,\ldots\) क्या समानांतर श्रेढ़ी है?
Is the sequence \(20,16,12,8,\ldots\) an arithmetic progression?
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A हाँ क्योंकि समान अंतर (-4) है / Yes because the common difference is (-4)
B नहीं क्योंकि पद घट रहे हैं / No because the terms are decreasing
C हाँ क्योंकि सभी पद धनात्मक हैं / Yes because all terms are positive
D नहीं क्योंकि पहला पद (20) है / No because the first term is (20)
Explanation opens after your attempt
Correct Answer
A. हाँ क्योंकि समान अंतर (-4) है / Yes because the common difference is (-4)
Step 1
Concept
Each time (4) is subtracted, so the common difference is (-4). A decreasing sequence can also be an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. हाँ क्योंकि समान अंतर (-4) है / Yes because the common difference is (-4). Each time (4) is subtracted, so the common difference is (-4). A decreasing sequence can also be an arithmetic progression.
Step 3
Exam Tip
हर बार (4) घट रहा है इसलिए समान अंतर (-4) है। घटती हुई श्रेढ़ी भी समानांतर श्रेढ़ी हो सकती है।
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समानांतर श्रेढ़ी \(3,8,13,18,\ldots\) का (10)वाँ पद क्या है?
What is the (10)th term of the arithmetic progression \(3,8,13,18,\ldots\)?
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A (43)
B (45)
C (46)
D (48)
Explanation opens after your attempt
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is D. (48). 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.
Step 3
Exam Tip
यहाँ (a=3) और (d=5), इसलिए (a_{10}=3+9(5)=48)। पद-संख्या से (1) कम अंतर जोड़े जाते हैं।
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यदि (a=11) और (d=-2) है, तो समानांतर श्रेढ़ी का चौथा पद क्या होगा?
If (a=11) and (d=-2), what will be the fourth term of the arithmetic progression?
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A (3)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
(a_4=11+3(-2)=5). Put the negative common difference in the formula with the correct sign.
Step 2
Why this answer is correct
The correct answer is C. (5). (a_4=11+3(-2)=5). Put the negative common difference in the formula with the correct sign.
Step 3
Exam Tip
(a_4=11+3(-2)=5)। ऋणात्मक समान अंतर को सूत्र में सही चिह्न के साथ रखें।
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समानांतर श्रेढ़ी \(6,10,14,18,\ldots\) में (38) कौन-सा पद है?
In the arithmetic progression \(6,10,14,18,\ldots\), which term is (38)?
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A (9)वाँ / (9)th
B (8)वाँ / (8)th
C (10)वाँ / (10)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
A. (9)वाँ / (9)th
Step 1
Concept
(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 \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (9)वाँ / (9)th. (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 \(a_n\).
Step 3
Exam Tip
(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।
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किस विकल्प में समानांतर श्रेढ़ी है?
Which option is an arithmetic progression?
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A \(2,4,8,16,\ldots\)
B \(1,5,9,13,\ldots\)
C \(3,6,12,24,\ldots\)
D \(1,4,9,16,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(1,5,9,13,\ldots\)
Step 1
Concept
In \(1,5,9,13,\ldots\), the common difference is (4). In an arithmetic progression, consecutive differences are equal.
Step 2
Why this answer is correct
The correct answer is B. \(1,5,9,13,\ldots\). In \(1,5,9,13,\ldots\), the common difference is (4). In an arithmetic progression, consecutive differences are equal.
Step 3
Exam Tip
\(1,5,9,13,\ldots\) में समान अंतर (4) है। समानांतर श्रेढ़ी में लगातार अंतर बराबर होते हैं।
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समानांतर श्रेढ़ी में \(a_1=4\) और \(a_6=24\) है। समान अंतर क्या है?
In an arithmetic progression, \(a_1=4\) and \(a_6=24\). What is the common difference?
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A (2)
B (3)
C (5)
D (4)
Explanation opens after your attempt
Step 1
Concept
\(a_6=a_1+5d\), so (24=4+5d) and (d=4). Count the number of gaps between the two terms.
Step 2
Why this answer is correct
The correct answer is D. (4). \(a_6=a_1+5d\), so (24=4+5d) and (d=4). Count the number of gaps between the two terms.
Step 3
Exam Tip
\(a_6=a_1+5d\), इसलिए (24=4+5d) और (d=4)। दो पदों के बीच अंतरों की संख्या गिनें।
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यदि किसी समानांतर श्रेढ़ी का (n)वाँ पद \(a_n=2n+5\) है, तो समान अंतर क्या होगा?
If the (n)th term of an arithmetic progression is \(a_n=2n+5\), what is the common difference?
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A (5)
B (7)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
In the linear form \(a_n=2n+5\), the coefficient of (n) is (2). In an arithmetic progression, this coefficient is the common difference.
Step 2
Why this answer is correct
The correct answer is C. (2). In the linear form \(a_n=2n+5\), the coefficient of (n) is (2). In an arithmetic progression, this coefficient is the common difference.
Step 3
Exam Tip
रैखिक रूप \(a_n=2n+5\) में (n) का गुणांक (2) है। समानांतर श्रेढ़ी में यह गुणांक समान अंतर होता है।
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समानांतर श्रेढ़ी \(15,12,9,6,\ldots\) का (7)वाँ पद क्या है?
What is the (7)th term of the arithmetic progression \(15,12,9,6,\ldots\)?
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A (-3)
B (0)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
Here (a=15) and (d=-3), so (a_7=15+6(-3)=-3). In a decreasing progression, terms may go below zero.
Step 2
Why this answer is correct
The correct answer is A. (-3). Here (a=15) and (d=-3), so (a_7=15+6(-3)=-3). In a decreasing progression, terms may go below zero.
Step 3
Exam Tip
यहाँ (a=15) और (d=-3), इसलिए (a_7=15+6(-3)=-3)। घटती श्रेढ़ी में पद शून्य से नीचे भी जा सकते हैं।
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समानांतर श्रेढ़ी \(2,7,12,17,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of the arithmetic progression \(2,7,12,17,\ldots\)?
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A (55)
B (60)
C (65)
D (70)
Explanation opens after your attempt
Step 1
Concept
The first (5) terms are (2,7,12,17,22), and their sum is (60). For small (n), writing and adding terms is quick.
Step 2
Why this answer is correct
The correct answer is B. (60). The first (5) terms are (2,7,12,17,22), and their sum is (60). For small (n), writing and adding terms is quick.
Step 3
Exam Tip
पहले (5) पद (2,7,12,17,22) हैं और योग (60) है। छोटे (n) में पद लिखकर जोड़ना तेज होता है।
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यदि समानांतर श्रेढ़ी में (a=9) और (d=6) है, तो तीसरा पद क्या होगा?
If an arithmetic progression has (a=9) and (d=6), what will be the third term?
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A (15)
B (18)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
(a_3=9+2(6)=21). Up to the third term, two common differences are added.
Step 2
Why this answer is correct
The correct answer is D. (21). (a_3=9+2(6)=21). Up to the third term, two common differences are added.
Step 3
Exam Tip
(a_3=9+2(6)=21)। तीसरे पद तक दो समान अंतर जोड़े जाते हैं।
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समानांतर श्रेढ़ी \(8,14,20,26,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the arithmetic progression \(8,14,20,26,\ldots\)?
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A \(a_n=6n+2\)
B \(a_n=8n+6\)
C \(a_n=6n+8\)
D \(a_n=2n+6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n+2\)
Step 1
Concept
The first term is (8) and the difference is (6), so (a_n=8+(n-1)6=6n+2). In the general term, (d) appears with (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n+2\). The first term is (8) and the difference is (6), so (a_n=8+(n-1)6=6n+2). In the general term, (d) appears with (n).
Step 3
Exam Tip
पहला पद (8) और अंतर (6) है इसलिए (a_n=8+(n-1)6=6n+2)। सामान्य पद में (d) का गुणांक (n) के साथ आता है।
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यदि समानांतर श्रेढ़ी का पहला पद (12) और चौथा पद (27) है, तो समान अंतर क्या है?
If the first term of an arithmetic progression is (12) and the fourth term is (27), what is the common difference?
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From \(a_4=12+3d=27\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.
Step 2
Why this answer is correct
The correct answer is C. (5). From \(a_4=12+3d=27\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.
Step 3
Exam Tip
\(a_4=12+3d=27\) से (3d=15) और (d=5)। चौथे पद तक तीन अंतर होते हैं।
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किस समानांतर श्रेढ़ी का पहला पद (4) और समान अंतर (7) है?
Which arithmetic progression has first term (4) and common difference (7)?
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A \(4,10,16,22,\ldots\)
B \(4,11,18,25,\ldots\)
C \(7,11,15,19,\ldots\)
D \(11,18,25,32,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(4,11,18,25,\ldots\)
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is B. \(4,11,18,25,\ldots\). 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.
Step 3
Exam Tip
पहला पद (4) है और हर बार (7) जोड़ने पर \(4,11,18,25,\ldots\) मिलता है। पहले पद और अंतर दोनों मिलाने चाहिए।
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समानांतर श्रेढ़ी \(4,9,14,19,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of the arithmetic progression \(4,9,14,19,\ldots\)?
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A (99)
B (100)
C (101)
D (105)
Explanation opens after your attempt
Step 1
Concept
The first (6) terms are (4,9,14,19,24,29), and their sum is (99). For small terms, listing and adding works well.
Step 2
Why this answer is correct
The correct answer is A. (99). The first (6) terms are (4,9,14,19,24,29), and their sum is (99). For small terms, listing and adding works well.
Step 3
Exam Tip
पहले (6) पद (4,9,14,19,24,29) हैं और उनका योग (99) है। छोटे पदों में सूची बनाकर जोड़ सकते हैं।
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यदि \(a_n=30-4n\) है, तो इस समानांतर श्रेढ़ी का पहला पद क्या है?
If \(a_n=30-4n\), what is the first term of this arithmetic progression?
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A (30)
B (26)
C (24)
D (22)
Explanation opens after your attempt
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is B. (26). 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.
Step 3
Exam Tip
पहले पद के लिए (n=1), इसलिए \(a_1=30-4=26\)। अनुक्रम में पहला पद निकालते समय (n=0) नहीं रखते।
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समानांतर श्रेढ़ी \(1,6,11,16,\ldots\) का (12)वाँ पद क्या होगा?
What will be the (12)th term of the arithmetic progression \(1,6,11,16,\ldots\)?
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A (51)
B (54)
C (56)
D (58)
Explanation opens after your attempt
Step 1
Concept
Here (a=1) and (d=5), so (a_{12}=1+11(5)=56). Up to the (12)th term, (11) differences are added.
Step 2
Why this answer is correct
The correct answer is C. (56). Here (a=1) and (d=5), so (a_{12}=1+11(5)=56). Up to the (12)th term, (11) differences are added.
Step 3
Exam Tip
यहाँ (a=1) और (d=5), इसलिए (a_{12}=1+11(5)=56)। (12)वें पद तक (11) अंतर जुड़ते हैं।
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यदि किसी समानांतर श्रेढ़ी में \(a_2=13\) और (d=4) है, तो \(a_1\) क्या होगा?
If an arithmetic progression has \(a_2=13\) and (d=4), what is \(a_1\)?
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A (5)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_2=a_1+d\), so \(a_1=13-4=9\). If the second term is given, move one common difference backward.
Step 2
Why this answer is correct
The correct answer is D. (9). \(a_2=a_1+d\), so \(a_1=13-4=9\). If the second term is given, move one common difference backward.
Step 3
Exam Tip
\(a_2=a_1+d\), इसलिए \(a_1=13-4=9\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं।
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कौन-सा अनुक्रम समानांतर श्रेढ़ी नहीं है?
Which sequence is not an arithmetic progression?
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A \(2,5,8,11,\ldots\)
B \(10,7,4,1,\ldots\)
C \(3,6,12,24,\ldots\)
D \(9,14,19,24,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(3,6,12,24,\ldots\)
Step 1
Concept
In \(3,6,12,24,\ldots\), the differences are (3,6,12), which are not equal. For an arithmetic progression, the difference must always be constant.
Step 2
Why this answer is correct
The correct answer is C. \(3,6,12,24,\ldots\). In \(3,6,12,24,\ldots\), the differences are (3,6,12), which are not equal. For an arithmetic progression, the difference must always be constant.
Step 3
Exam Tip
\(3,6,12,24,\ldots\) में अंतर (3,6,12) हैं, जो बराबर नहीं हैं। समानांतर श्रेढ़ी के लिए अंतर हमेशा समान होना चाहिए।
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समानांतर श्रेढ़ी \(40,35,30,25,\ldots\) में (5) कौन-सा पद है?
In the arithmetic progression \(40,35,30,25,\ldots\), which term is (5)?
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A (6)वाँ / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
Explanation opens after your attempt
Correct Answer
C. (8)वाँ / (8)th
Step 1
Concept
(a_n=40+(n-1)(-5)), and (40-5(n-1)=5) gives (n=8). In a decreasing progression, the position is still positive.
Step 2
Why this answer is correct
The correct answer is C. (8)वाँ / (8)th. (a_n=40+(n-1)(-5)), and (40-5(n-1)=5) gives (n=8). In a decreasing progression, the position is still positive.
Step 3
Exam Tip
(a_n=40+(n-1)(-5)) और (40-5(n-1)=5) से (n=8)। घटती श्रेढ़ी में भी पद-संख्या धनात्मक होती है।
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यदि समानांतर श्रेढ़ी का पहला पद (3) और सातवाँ पद (33) है, तो समान अंतर क्या है?
If the first term of an arithmetic progression is (3) and the seventh term is (33), what is the common difference?
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#progressions
#arithmetic-progression
#common-difference
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From \(a_7=3+6d=33\), (6d=30) and (d=5). Up to the seventh term, there are six gaps.
Step 2
Why this answer is correct
The correct answer is B. (5). From \(a_7=3+6d=33\), (6d=30) and (d=5). Up to the seventh term, there are six gaps.
Step 3
Exam Tip
\(a_7=3+6d=33\) से (6d=30) और (d=5)। सातवें पद तक छह अंतर होते हैं।
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समानांतर श्रेढ़ी \(12,17,22,27,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the arithmetic progression \(12,17,22,27,\ldots\)?
#sequences
#progressions
#arithmetic-progression
#general-term
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A \(a_n=5n+7\)
B \(a_n=7n+5\)
C \(a_n=5n+12\)
D \(a_n=12n+5\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n+7\)
Step 1
Concept
Here (a=12) and (d=5), so (a_n=12+(n-1)5=5n+7). Use (n-1) while forming the general term.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n+7\). Here (a=12) and (d=5), so (a_n=12+(n-1)5=5n+7). Use (n-1) while forming the general term.
Step 3
Exam Tip
यहाँ (a=12) और (d=5), इसलिए (a_n=12+(n-1)5=5n+7)। सामान्य पद बनाते समय (n-1) का उपयोग करें।
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यदि \(a_n=4n-1\) है, तो इस समानांतर श्रेढ़ी का (8)वाँ पद क्या है?
If \(a_n=4n-1\), what is the (8)th term of this arithmetic progression?
#sequences
#progressions
#arithmetic-progression
#nth-term
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A (27)
B (29)
C (31)
D (33)
Explanation opens after your attempt
Step 1
Concept
(a_8=4(8)-1=31). Substitute (n=8) directly in the given (n)th term.
Step 2
Why this answer is correct
The correct answer is C. (31). (a_8=4(8)-1=31). Substitute (n=8) directly in the given (n)th term.
Step 3
Exam Tip
(a_8=4(8)-1=31)। दिए हुए (n)वें पद में सीधे (n=8) रखें।
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समानांतर श्रेढ़ी \(7,10,13,16,\ldots\) के पहले (4) पदों का योग क्या है?
What is the sum of the first (4) terms of the arithmetic progression \(7,10,13,16,\ldots\)?
#sequences
#progressions
#arithmetic-progression
#sum
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A (40)
B (44)
C (46)
D (48)
Explanation opens after your attempt
Step 1
Concept
The sum of the first (4) terms is (7+10+13+16=46). If there are few terms, direct addition is simple.
Step 2
Why this answer is correct
The correct answer is C. (46). The sum of the first (4) terms is (7+10+13+16=46). If there are few terms, direct addition is simple.
Step 3
Exam Tip
पहले (4) पदों का योग (7+10+13+16=46) है। कम पद हों तो सीधे जोड़ना सरल है।
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किस समानांतर श्रेढ़ी का समान अंतर (-6) है?
Which arithmetic progression has common difference (-6)?
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#progressions
#arithmetic-progression
#negative-difference
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A \(18,12,6,0,\ldots\)
B \(6,12,18,24,\ldots\)
C \(18,13,8,3,\ldots\)
D \(0,6,12,18,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(18,12,6,0,\ldots\)
Step 1
Concept
In \(18,12,6,0,\ldots\), (6) is subtracted each time, so (d=-6). The sign is very important in common difference.
Step 2
Why this answer is correct
The correct answer is A. \(18,12,6,0,\ldots\). In \(18,12,6,0,\ldots\), (6) is subtracted each time, so (d=-6). The sign is very important in common difference.
Step 3
Exam Tip
\(18,12,6,0,\ldots\) में हर बार (6) घट रहा है, इसलिए (d=-6)। समान अंतर में चिह्न बहुत महत्वपूर्ण है।
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यदि समानांतर श्रेढ़ी में \(a_4=18\) और (d=3) है, तो \(a_9\) क्या होगा?
If an arithmetic progression has \(a_4=18\) and (d=3), what will be \(a_9\)?
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#progressions
#arithmetic-progression
#nth-term
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A (30)
B (31)
C (32)
D (33)
Explanation opens after your attempt
Step 1
Concept
From \(a_4\) to \(a_9\), there are (5) gaps, so (a_9=18+5(3)=33). Moving forward from a nearby term is a quick method.
Step 2
Why this answer is correct
The correct answer is D. (33). From \(a_4\) to \(a_9\), there are (5) gaps, so (a_9=18+5(3)=33). Moving forward from a nearby term is a quick method.
Step 3
Exam Tip
\(a_9\) तक \(a_4\) से (5) अंतर आगे हैं, इसलिए (a_9=18+5(3)=33)। पास के पद से आगे बढ़ना तेज तरीका है।
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समानांतर श्रेढ़ी \(100,90,80,70,\ldots\) का (11)वाँ पद क्या है?
What is the (11)th term of the arithmetic progression \(100,90,80,70,\ldots\)?
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#progressions
#arithmetic-progression
#decreasing-ap
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A (0)
B (10)
C (20)
D (30)
Explanation opens after your attempt
Step 1
Concept
Here (a=100) and (d=-10), so (a_{11}=100+10(-10)=0). Up to the (11)th term, (10) gaps are used.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (a=100) and (d=-10), so (a_{11}=100+10(-10)=0). Up to the (11)th term, (10) gaps are used.
Step 3
Exam Tip
यहाँ (a=100) और (d=-10), इसलिए (a_{11}=100+10(-10)=0)। (11)वें पद तक (10) अंतर लगते हैं।
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यदि \(a_n=9n+2\) है, तो समानांतर श्रेढ़ी का पहला पद क्या है?
If \(a_n=9n+2\), what is the first term of the arithmetic progression?
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#progressions
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#first-term
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A (9)
B (11)
C (13)
D (2)
Explanation opens after your attempt
Step 1
Concept
For the first term (n=1), so \(a_1=9+2=11\). To find the first term from \(a_n\), put (n=1).
Step 2
Why this answer is correct
The correct answer is B. (11). For the first term (n=1), so \(a_1=9+2=11\). To find the first term from \(a_n\), put (n=1).
Step 3
Exam Tip
पहले पद के लिए (n=1), इसलिए \(a_1=9+2=11\)। \(a_n\) में पहला पद निकालने के लिए (n=1) रखें।
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किस विकल्प में (a=5) और (d=2) वाली समानांतर श्रेढ़ी के पहले चार पद हैं?
Which option has the first four terms of the arithmetic progression with (a=5) and (d=2)?
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#progressions
#arithmetic-progression
#sequence-formation
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A (5,7,9,11)
B (2,5,8,11)
C (5,10,15,20)
D (7,9,11,13)
Explanation opens after your attempt
Correct Answer
A. (5,7,9,11)
Step 1
Concept
The first term is (5), and adding (2) each time gives (5,7,9,11). Form terms directly from the given (a) and (d).
Step 2
Why this answer is correct
The correct answer is A. (5,7,9,11). The first term is (5), and adding (2) each time gives (5,7,9,11). Form terms directly from the given (a) and (d).
Step 3
Exam Tip
पहला पद (5) है और हर बार (2) जोड़ने पर (5,7,9,11) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं।
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समानांतर श्रेढ़ी \(13,19,25,31,\ldots\) में (61) कौन-सा पद है?
In the arithmetic progression \(13,19,25,31,\ldots\), which term is (61)?
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#progressions
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
C. (9)वाँ / (9)th
Step 1
Concept
From (13+(n-1)6=61), (6(n-1)=48) and (n=9). Solve the linear equation to find the position of a term.
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. From (13+(n-1)6=61), (6(n-1)=48) and (n=9). Solve the linear equation to find the position of a term.
Step 3
Exam Tip
(13+(n-1)6=61) से (6(n-1)=48) और (n=9)। पद की स्थिति के लिए रैखिक समीकरण हल करें।
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यदि समानांतर श्रेढ़ी का तीसरा पद (14) और पाँचवाँ पद (22) है, तो समान अंतर क्या है?
If the third term of an arithmetic progression is (14) and the fifth term is (22), what is the common difference?
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#common-difference
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From the third to the fifth term there are (2) gaps and the increase is (8), so (d=4). Count the number of gaps between terms.
Step 2
Why this answer is correct
The correct answer is C. (4). From the third to the fifth term there are (2) gaps and the increase is (8), so (d=4). Count the number of gaps between terms.
Step 3
Exam Tip
तीसरे से पाँचवें पद तक (2) अंतर हैं और वृद्धि (8) है, इसलिए (d=4)। पदों के बीच अंतरालों की संख्या गिनें।
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समानांतर श्रेढ़ी \(22,18,14,10,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the arithmetic progression \(22,18,14,10,\ldots\)?
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#progressions
#arithmetic-progression
#general-term
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A \(a_n=26-4n\)
B \(a_n=22-4n\)
C \(a_n=4n+18\)
D \(a_n=26+4n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=26-4n\)
Step 1
Concept
The first term is (22) and (d=-4), so (a_n=22+(n-1)(-4)=26-4n). Keep (d) negative in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=26-4n\). The first term is (22) and (d=-4), so (a_n=22+(n-1)(-4)=26-4n). Keep (d) negative in a decreasing sequence.
Step 3
Exam Tip
पहला पद (22) और (d=-4) है इसलिए (a_n=22+(n-1)(-4)=26-4n)। घटते क्रम में (d) को ऋणात्मक रखें।
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समानांतर श्रेढ़ी \(2,8,14,20,\ldots\) के पहले (3) पदों का औसत क्या है?
What is the average of the first (3) terms of the arithmetic progression \(2,8,14,20,\ldots\)?
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#average
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A (6)
B (7)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is C. (8). 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.
Step 3
Exam Tip
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।
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यदि किसी समानांतर श्रेढ़ी में (a=6) और \(a_5=30\) है, तो (d) क्या होगा?
If an arithmetic progression has (a=6) and \(a_5=30\), what is (d)?
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#progressions
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#common-difference
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From \(a_5=6+4d=30\), (4d=24) and (d=6). Up to the fifth term, four common differences are added.
Step 2
Why this answer is correct
The correct answer is C. (6). From \(a_5=6+4d=30\), (4d=24) and (d=6). Up to the fifth term, four common differences are added.
Step 3
Exam Tip
\(a_5=6+4d=30\) से (4d=24) और (d=6)। पाँचवें पद तक चार समान अंतर जुड़ते हैं।
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किस विकल्प में (d=0) वाली समानांतर श्रेढ़ी है?
Which option is an arithmetic progression with (d=0)?
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#progressions
#arithmetic-progression
#zero-difference
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A \(4,4,4,4,\ldots\)
B \(0,1,2,3,\ldots\)
C \(5,10,15,20,\ldots\)
D \(9,6,3,0,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(4,4,4,4,\ldots\)
Step 1
Concept
All terms are (4), so every difference is (0). A constant sequence is also an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. \(4,4,4,4,\ldots\). All terms are (4), so every difference is (0). A constant sequence is also an arithmetic progression.
Step 3
Exam Tip
सभी पद (4) हैं इसलिए हर अंतर (0) है। स्थिर अनुक्रम भी समानांतर श्रेढ़ी होता है।
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समानांतर श्रेढ़ी \(17,23,29,35,\ldots\) का (6)वाँ पद क्या है?
What is the (6)th term of the arithmetic progression \(17,23,29,35,\ldots\)?
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#progressions
#arithmetic-progression
#nth-term
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A (41)
B (43)
C (47)
D (49)
Explanation opens after your attempt
Step 1
Concept
Here (a=17) and (d=6), so (a_6=17+5(6)=47). Up to the (6)th term, five gaps are added.
Step 2
Why this answer is correct
The correct answer is C. (47). Here (a=17) and (d=6), so (a_6=17+5(6)=47). Up to the (6)th term, five gaps are added.
Step 3
Exam Tip
यहाँ (a=17) और (d=6), इसलिए (a_6=17+5(6)=47)। (6)वें पद तक पाँच अंतर जुड़ते हैं।
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यदि \(a_n=5n+3\) है, तो \(a_2+a_4\) का मान क्या है?
If \(a_n=5n+3\), what is the value of \(a_2+a_4\)?
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#progressions
#arithmetic-progression
#sum-of-terms
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A (30)
B (31)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(a_2=13\) and \(a_4=23\), so the sum is (36). Find both terms separately before adding.
Step 2
Why this answer is correct
The correct answer is D. (36). \(a_2=13\) and \(a_4=23\), so the sum is (36). Find both terms separately before adding.
Step 3
Exam Tip
\(a_2=13\) और \(a_4=23\), इसलिए योग (36) है। जोड़ने से पहले दोनों पद अलग निकालें।
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समानांतर श्रेढ़ी \(50,45,40,35,\ldots\) का कौन-सा पद (0) है?
Which term of the arithmetic progression \(50,45,40,35,\ldots\) is (0)?
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#arithmetic-progression
#term-position
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A (9)वाँ / (9)th
B (10)वाँ / (10)th
C (11)वाँ / (11)th
D (12)वाँ / (12)th
Explanation opens after your attempt
Correct Answer
C. (11)वाँ / (11)th
Step 1
Concept
From (50+(n-1)(-5)=0), (n=11). Zero can also be a term of a progression.
Step 2
Why this answer is correct
The correct answer is C. (11)वाँ / (11)th. From (50+(n-1)(-5)=0), (n=11). Zero can also be a term of a progression.
Step 3
Exam Tip
(50+(n-1)(-5)=0) से (n=11)। शून्य भी श्रेढ़ी का पद हो सकता है।
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एक समानांतर श्रेढ़ी में (a=2) और (d=9) है। \(a_8\) क्या होगा?
In an arithmetic progression, (a=2) and (d=9). What will be \(a_8\)?
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#progressions
#arithmetic-progression
#nth-term
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A (56)
B (60)
C (63)
D (65)
Explanation opens after your attempt
Step 1
Concept
(a_8=2+7(9)=65). Up to the eighth term, seven common differences are added.
Step 2
Why this answer is correct
The correct answer is D. (65). (a_8=2+7(9)=65). Up to the eighth term, seven common differences are added.
Step 3
Exam Tip
(a_8=2+7(9)=65)। आठवें पद तक सात समान अंतर जोड़े जाते हैं।
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समानांतर श्रेढ़ी \(3,13,23,33,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of the arithmetic progression \(3,13,23,33,\ldots\)?
#sequences
#progressions
#arithmetic-progression
#sum
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A (105)
B (110)
C (115)
D (125)
Explanation opens after your attempt
Step 1
Concept
The first (5) terms are (3,13,23,33,43), and the sum is (115). Write the terms in correct order and add them.
Step 2
Why this answer is correct
The correct answer is C. (115). The first (5) terms are (3,13,23,33,43), and the sum is (115). Write the terms in correct order and add them.
Step 3
Exam Tip
पहले (5) पद (3,13,23,33,43) हैं और योग (115) है। पदों को सही क्रम में लिखकर जोड़ें।
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यदि \(a_1=25\) और (d=-5) है, तो \(a_6\) क्या होगा?
If \(a_1=25\) and (d=-5), what is \(a_6\)?
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#progressions
#arithmetic-progression
#negative-difference
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A (0)
B (5)
C (10)
D (15)
Explanation opens after your attempt
Step 1
Concept
(a_6=25+5(-5)=0). Handle subtraction correctly with a negative difference.
Step 2
Why this answer is correct
The correct answer is A. (0). (a_6=25+5(-5)=0). Handle subtraction correctly with a negative difference.
Step 3
Exam Tip
(a_6=25+5(-5)=0)। ऋणात्मक अंतर के साथ घटाव सही तरीके से करें।
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किस समानांतर श्रेढ़ी का (n)वाँ पद \(a_n=3n+8\) है?
Which arithmetic progression has (n)th term \(a_n=3n+8\)?
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#progressions
#arithmetic-progression
#sequence-from-rule
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A \(8,11,14,17,\ldots\)
B \(11,14,17,20,\ldots\)
C \(3,11,19,27,\ldots\)
D \(10,13,16,19,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(11,14,17,20,\ldots\)
Step 1
Concept
Putting (n=1,2,3,4) gives (11,14,17,20). Form the first few terms from the rule and match.
Step 2
Why this answer is correct
The correct answer is B. \(11,14,17,20,\ldots\). Putting (n=1,2,3,4) gives (11,14,17,20). Form the first few terms from the rule and match.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (11,14,17,20) मिलते हैं। नियम से पहले कुछ पद बनाकर मिलाएं।
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समानांतर श्रेढ़ी \(6,15,24,33,\ldots\) में (69) कौन-सा पद है?
In the arithmetic progression \(6,15,24,33,\ldots\), which term is (69)?
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#progressions
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#term-position
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
B. (8)वाँ / (8)th
Step 1
Concept
From (6+(n-1)9=69), (9(n-1)=63) and (n=8). Do not forget (n-1) while finding the position.
Step 2
Why this answer is correct
The correct answer is B. (8)वाँ / (8)th. From (6+(n-1)9=69), (9(n-1)=63) and (n=8). Do not forget (n-1) while finding the position.
Step 3
Exam Tip
(6+(n-1)9=69) से (9(n-1)=63) और (n=8)। पद की स्थिति निकालते समय (n-1) को न भूलें।
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यदि समानांतर श्रेढ़ी में \(a_5=28\) और (d=4) है, तो \(a_2\) क्या होगा?
If an arithmetic progression has \(a_5=28\) and (d=4), what is \(a_2\)?
#sequences
#progressions
#arithmetic-progression
#term-relation
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A (14)
B (16)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
From \(a_5\) to \(a_2\), move back three gaps, so (a_2=28-3(4)=16). When moving backward, subtract the common difference.
Step 2
Why this answer is correct
The correct answer is B. (16). From \(a_5\) to \(a_2\), move back three gaps, so (a_2=28-3(4)=16). When moving backward, subtract the common difference.
Step 3
Exam Tip
\(a_5\) से \(a_2\) तक तीन अंतर पीछे जाना है, इसलिए (a_2=28-3(4)=16)। पीछे जाते समय समान अंतर घटाएं।
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समानांतर श्रेढ़ी \(11,8,5,2,\ldots\) का पहला ऋणात्मक पद कौन-सा है?
What is the first negative term of the arithmetic progression \(11,8,5,2,\ldots\)?
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A (4)वाँ / (4)th
B (5)वाँ / (5)th
C (6)वाँ / (6)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
C. (6)वाँ / (6)th
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is C. (6)वाँ / (6)th. 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.
Step 3
Exam Tip
पद \(11,8,5,2,-1,\ldots\) नहीं बल्कि (5)वाँ पद (-1) है। इसलिए पहला ऋणात्मक पद (5)वाँ है।
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यदि समानांतर श्रेढ़ी के लगातार तीन पद (x-2), (x+3), (2x-1) हैं, तो (x) का मान क्या है?
If three consecutive terms of an arithmetic progression are (x-2), (x+3), (2x-1), what is the value of (x)?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
In an arithmetic progression, (2(x+3)=(x-2)+(2x-1)), which gives (x=9). The middle term is the average of the two adjacent terms.
Step 2
Why this answer is correct
The correct answer is D. (7). In an arithmetic progression, (2(x+3)=(x-2)+(2x-1)), which gives (x=9). The middle term is the average of the two adjacent terms.
Step 3
Exam Tip
समानांतर श्रेढ़ी में (2(x+3)=(x-2)+(2x-1)), इससे (x=9) मिलता है। बीच का पद दो बराबर हिस्सों में होता है।
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समानांतर श्रेढ़ी \(4,4,4,4,\ldots\) का (20)वाँ पद क्या है?
What is the (20)th term of the arithmetic progression \(4,4,4,4,\ldots\)?
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A (0)
B (4)
C (20)
D (80)
Explanation opens after your attempt
Step 1
Concept
In this progression (d=0), so every term is (4). In a constant arithmetic progression, all terms are equal.
Step 2
Why this answer is correct
The correct answer is B. (4). In this progression (d=0), so every term is (4). In a constant arithmetic progression, all terms are equal.
Step 3
Exam Tip
इस श्रेढ़ी में (d=0) है, इसलिए हर पद (4) है। स्थिर समानांतर श्रेढ़ी में सभी पद बराबर होते हैं।
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यदि \(a_n=18-2n\) है, तो \(a_3+a_6\) का मान क्या है?
If \(a_n=18-2n\), what is the value of \(a_3+a_6\)?
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#sum-of-terms
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A (22)
B (24)
C (26)
D (28)
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Step 1
Concept
\(a_3=12\) and \(a_6=6\), so the sum is (18). Calculate both terms separately.
Step 2
Why this answer is correct
The correct answer is B. (24). \(a_3=12\) and \(a_6=6\), so the sum is (18). Calculate both terms separately.
Step 3
Exam Tip
\(a_3=12\) और \(a_6=6\), इसलिए योग (18) नहीं बल्कि (18) है। गणना में दोनों पद अलग-अलग निकालें।
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समानांतर श्रेढ़ी \(21,28,35,42,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the arithmetic progression \(21,28,35,42,\ldots\)?
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#general-term
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A \(a_n=7n+14\)
B \(a_n=14n+7\)
C \(a_n=7n+21\)
D \(a_n=21n+7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7n+14\)
Step 1
Concept
The first term is (21) and (d=7), so (a_n=21+(n-1)7=7n+14). You can also check an option by putting (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=7n+14\). The first term is (21) and (d=7), so (a_n=21+(n-1)7=7n+14). You can also check an option by putting (n=1).
Step 3
Exam Tip
पहला पद (21) और (d=7) है इसलिए (a_n=21+(n-1)7=7n+14)। विकल्प को (n=1) रखकर भी जांच सकते हैं।
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