अनुक्रम \(14,20,26,32,\ldots\) में समान अंतर क्या है?
What is the common difference in the sequence \(14,20,26,32,\ldots\)?
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
The difference between consecutive terms is (20-14=6). 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. (6). The difference between consecutive terms is (20-14=6). To find the common difference subtract the first term from the second term.
Step 3
Exam Tip
लगातार पदों का अंतर (20-14=6) है। समान अंतर निकालने के लिए दूसरे पद से पहला पद घटाएं।
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यदि किसी समानांतर श्रेढ़ी में पहला पद (9) और समान अंतर (4) है, तो (8)वाँ पद क्या होगा?
If an arithmetic progression has first term (9) and common difference (4), what is the (8)th term?
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A (33)
B (35)
C (37)
D (39)
Explanation opens after your attempt
Step 1
Concept
(a_8=9+(8-1)4=37). Use (a_n=a+(n-1)d) for the (n)th term.
Step 2
Why this answer is correct
The correct answer is C. (37). (a_8=9+(8-1)4=37). Use (a_n=a+(n-1)d) for the (n)th term.
Step 3
Exam Tip
(a_8=9+(8-1)4=37)। (n)वें पद के लिए (a_n=a+(n-1)d) का प्रयोग करें।
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समानांतर श्रेढ़ी \(35,31,27,23,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the arithmetic progression \(35,31,27,23,\ldots\)?
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A \(a_n=35-4n\)
B \(a_n=39-4n\)
C \(a_n=4n+31\)
D \(a_n=39+4n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=39-4n\)
Step 1
Concept
The first term is (35) and the difference is (-4), so (a_n=35+(n-1)(-4)=39-4n). In a decreasing progression the common difference is negative.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=39-4n\). The first term is (35) and the difference is (-4), so (a_n=35+(n-1)(-4)=39-4n). In a decreasing progression the common difference is negative.
Step 3
Exam Tip
पहला पद (35) और अंतर (-4) है इसलिए (a_n=35+(n-1)(-4)=39-4n)। घटती श्रेढ़ी में समान अंतर ऋणात्मक होता है।
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अनुक्रम \(2,5,9,14,\ldots\) समानांतर श्रेढ़ी क्यों नहीं है?
Why is the sequence \(2,5,9,14,\ldots\) not an arithmetic progression?
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A क्योंकि अंतर (3,4,5) बराबर नहीं हैं / Because the differences (3,4,5) are not equal
B क्योंकि पहला पद (2) है / Because the first term is (2)
C क्योंकि पद बढ़ रहे हैं / Because the terms are increasing
D क्योंकि इसमें चार पद हैं / Because it has four terms
Explanation opens after your attempt
Correct Answer
A. क्योंकि अंतर (3,4,5) बराबर नहीं हैं / Because the differences (3,4,5) are not equal
Step 1
Concept
The consecutive differences are (3,4,5), which are not equal. An arithmetic progression must have the same difference each time.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि अंतर (3,4,5) बराबर नहीं हैं / Because the differences (3,4,5) are not equal. The consecutive differences are (3,4,5), which are not equal. An arithmetic progression must have the same difference each time.
Step 3
Exam Tip
लगातार अंतर (3,4,5) हैं जो समान नहीं हैं। समानांतर श्रेढ़ी में हर बार समान अंतर होना चाहिए।
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यदि (a=6) और (d=7) है, तो समानांतर श्रेढ़ी का (5)वाँ पद क्या होगा?
If (a=6) and (d=7), what will be the (5)th term of the arithmetic progression?
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A (27)
B (34)
C (35)
D (41)
Explanation opens after your attempt
Step 1
Concept
(a_5=6+(5-1)7=34). Up to the fifth term four common differences are added.
Step 2
Why this answer is correct
The correct answer is B. (34). (a_5=6+(5-1)7=34). Up to the fifth term four common differences are added.
Step 3
Exam Tip
(a_5=6+(5-1)7=34)। पाँचवें पद तक चार समान अंतर जुड़ते हैं।
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समानांतर श्रेढ़ी \(8,13,18,23,\ldots\) में (48) कौन-सा पद है?
In the arithmetic progression \(8,13,18,23,\ldots\), which term is (48)?
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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 (8+(n-1)5=48), (n=9). To find the position set the given term equal to \(a_n\).
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. From (8+(n-1)5=48), (n=9). To find the position set the given term equal to \(a_n\).
Step 3
Exam Tip
(8+(n-1)5=48) से (n=9) मिलता है। पद का स्थान निकालने के लिए दिए पद को \(a_n\) के बराबर रखें।
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यदि \(a_n=3n+2\) है, तो पहले चार पद कौन-से होंगे?
If \(a_n=3n+2\), what will be the first four terms?
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A (5,8,11,14)
B (3,6,9,12)
C (2,5,8,11)
D (6,9,12,15)
Explanation opens after your attempt
Correct Answer
A. (5,8,11,14)
Step 1
Concept
Putting (n=1,2,3,4) gives (5,8,11,14). When forming terms from a rule start (n) from (1).
Step 2
Why this answer is correct
The correct answer is A. (5,8,11,14). Putting (n=1,2,3,4) gives (5,8,11,14). When forming terms from a rule start (n) from (1).
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (5,8,11,14) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें।
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समानांतर श्रेढ़ी में \(a_1=12\) और \(a_6=32\) है। समान अंतर क्या है?
In an arithmetic progression \(a_1=12\) and \(a_6=32\). 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
\(a_6=a_1+5d\), so (32=12+5d) and (d=4). Count the number of gaps between the two terms.
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_6=a_1+5d\), so (32=12+5d) and (d=4). Count the number of gaps between the two terms.
Step 3
Exam Tip
\(a_6=a_1+5d\) इसलिए (32=12+5d) और (d=4)। दो पदों के बीच अंतरालों की संख्या गिनें।
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समानांतर श्रेढ़ी \(5,12,19,26,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of the arithmetic progression \(5,12,19,26,\ldots\)?
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A (85)
B (90)
C (95)
D (100)
Explanation opens after your attempt
Step 1
Concept
The first (5) terms are (5,12,19,26,33), and their sum is (95). For a small number of terms direct listing and addition is simple.
Step 2
Why this answer is correct
The correct answer is C. (95). The first (5) terms are (5,12,19,26,33), and their sum is (95). For a small number of terms direct listing and addition is simple.
Step 3
Exam Tip
पहले (5) पद (5,12,19,26,33) हैं और योग (95) है। कम पद हों तो सीधे लिखकर जोड़ना सरल है।
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यदि \(a_n=42-6n\) है, तो इस समानांतर श्रेढ़ी का समान अंतर क्या है?
If \(a_n=42-6n\), what is the common difference of this arithmetic progression?
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A (-6)
B (6)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
In the linear form the coefficient of (n) is (-6), so the common difference is (-6). Always check the sign of the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (-6). In the linear form the coefficient of (n) is (-6), so the common difference is (-6). Always check the sign of the coefficient.
Step 3
Exam Tip
रैखिक रूप में (n) का गुणांक (-6) है इसलिए समान अंतर (-6) है। गुणांक का चिह्न जरूर देखें।
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कौन-सा अनुक्रम समानांतर श्रेढ़ी है?
Which sequence is an arithmetic progression?
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A \(3,6,12,24,\ldots\)
B \(4,9,16,25,\ldots\)
C \(7,11,15,19,\ldots\)
D \(2,4,8,16,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(7,11,15,19,\ldots\)
Step 1
Concept
In \(7,11,15,19,\ldots\), the common difference is (4). In an arithmetic progression consecutive differences are equal.
Step 2
Why this answer is correct
The correct answer is C. \(7,11,15,19,\ldots\). In \(7,11,15,19,\ldots\), the common difference is (4). In an arithmetic progression consecutive differences are equal.
Step 3
Exam Tip
\(7,11,15,19,\ldots\) में समान अंतर (4) है। समानांतर श्रेढ़ी में लगातार अंतर बराबर होते हैं।
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यदि समानांतर श्रेढ़ी का पहला पद (18) और चौथा पद (30) है, तो समान अंतर क्या है?
If the first term of an arithmetic progression is (18) and the fourth term is (30), what is the common difference?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From \(a_4=18+3d=30\), (3d=12) and (d=4). Up to the fourth term there are three gaps.
Step 2
Why this answer is correct
The correct answer is C. (4). From \(a_4=18+3d=30\), (3d=12) and (d=4). Up to the fourth term there are three gaps.
Step 3
Exam Tip
\(a_4=18+3d=30\) से (3d=12) और (d=4)। चौथे पद तक तीन अंतर होते हैं।
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समानांतर श्रेढ़ी \(11,17,23,29,\ldots\) का (12)वाँ पद क्या है?
What is the (12)th term of the arithmetic progression \(11,17,23,29,\ldots\)?
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A (71)
B (73)
C (77)
D (79)
Explanation opens after your attempt
Step 1
Concept
Here (a=11) and (d=6), so (a_{12}=11+11(6)=77). Up to the (12)th term (11) gaps are added.
Step 2
Why this answer is correct
The correct answer is C. (77). Here (a=11) and (d=6), so (a_{12}=11+11(6)=77). Up to the (12)th term (11) gaps are added.
Step 3
Exam Tip
यहाँ (a=11) और (d=6), इसलिए (a_{12}=11+11(6)=77)। (12)वें पद तक (11) अंतर जुड़ते हैं।
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यदि \(a_2=15\) और (d=5) है, तो \(a_1\) क्या होगा?
If \(a_2=15\) and (d=5), what is \(a_1\)?
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A (5)
B (10)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(a_2=a_1+d\), so \(a_1=15-5=10\). If the second term is given move one common difference backward.
Step 2
Why this answer is correct
The correct answer is B. (10). \(a_2=a_1+d\), so \(a_1=15-5=10\). If the second term is given move one common difference backward.
Step 3
Exam Tip
\(a_2=a_1+d\) इसलिए \(a_1=15-5=10\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं।
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समानांतर श्रेढ़ी \(28,24,20,16,\ldots\) का (9)वाँ पद क्या होगा?
What will be the (9)th term of the arithmetic progression \(28,24,20,16,\ldots\)?
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A (-4)
B (-2)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
Here (a=28) and (d=-4), so (a_9=28+8(-4)=-4). In a decreasing progression terms can become negative.
Step 2
Why this answer is correct
The correct answer is A. (-4). Here (a=28) and (d=-4), so (a_9=28+8(-4)=-4). In a decreasing progression terms can become negative.
Step 3
Exam Tip
यहाँ (a=28) और (d=-4), इसलिए (a_9=28+8(-4)=-4)। घटती श्रेढ़ी में पद ऋणात्मक भी हो सकते हैं।
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किस समानांतर श्रेढ़ी का पहला पद (6) और समान अंतर (-3) है?
Which arithmetic progression has first term (6) and common difference (-3)?
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A \(6,9,12,15,\ldots\)
B \(3,6,9,12,\ldots\)
C \(6,3,0,-3,\ldots\)
D \(9,6,3,0,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(6,3,0,-3,\ldots\)
Step 1
Concept
The first term is (6), and (3) is subtracted each time. Therefore the common difference is (-3).
Step 2
Why this answer is correct
The correct answer is C. \(6,3,0,-3,\ldots\). The first term is (6), and (3) is subtracted each time. Therefore the common difference is (-3).
Step 3
Exam Tip
पहला पद (6) है और हर बार (3) घट रहा है। इसलिए समान अंतर (-3) है।
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यदि \(a_n=7n-2\) है, तो पहला पद क्या है?
If \(a_n=7n-2\), what is the first term?
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A (5)
B (7)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
For the first term (n=1), so \(a_1=7-2=5\). Put (n=1) to find the first term.
Step 2
Why this answer is correct
The correct answer is A. (5). For the first term (n=1), so \(a_1=7-2=5\). Put (n=1) to find the first term.
Step 3
Exam Tip
पहले पद के लिए (n=1), इसलिए \(a_1=7-2=5\)। पहला पद निकालने में (n=1) रखें।
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समानांतर श्रेढ़ी \(16,21,26,31,\ldots\) में (56) कौन-सा पद है?
In the arithmetic progression \(16,21,26,31,\ldots\), which term is (56)?
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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 (16+(n-1)5=56), (n=9). Solve the simple 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 (16+(n-1)5=56), (n=9). Solve the simple linear equation to find the position of a term.
Step 3
Exam Tip
(16+(n-1)5=56) से (n=9) मिलता है। पद की स्थिति के लिए सरल रैखिक समीकरण हल करें।
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समानांतर श्रेढ़ी \(9,15,21,27,\ldots\) के पहले (4) पदों का योग क्या है?
What is the sum of the first (4) terms of the arithmetic progression \(9,15,21,27,\ldots\)?
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A (66)
B (72)
C (78)
D (84)
Explanation opens after your attempt
Step 1
Concept
The sum of the first (4) terms is (9+15+21+27=72). If there are few terms direct addition is easy.
Step 2
Why this answer is correct
The correct answer is B. (72). The sum of the first (4) terms is (9+15+21+27=72). If there are few terms direct addition is easy.
Step 3
Exam Tip
पहले (4) पदों का योग (9+15+21+27=72) है। कम पद हों तो सीधे जोड़ना आसान है।
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यदि (a=25) और (d=-5) है, तो \(a_7\) क्या होगा?
If (a=25) and (d=-5), what will \(a_7\) be?
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A (-10)
B (-5)
C (0)
D (5)
Explanation opens after your attempt
Step 1
Concept
(a_7=25+6(-5)=-5). Keep the negative common difference with the correct sign.
Step 2
Why this answer is correct
The correct answer is B. (-5). (a_7=25+6(-5)=-5). Keep the negative common difference with the correct sign.
Step 3
Exam Tip
(a_7=25+6(-5)=-5)। ऋणात्मक समान अंतर को सही चिह्न के साथ रखें।
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समानांतर श्रेढ़ी \(4,11,18,25,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the arithmetic progression \(4,11,18,25,\ldots\)?
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A \(a_n=7n-3\)
B \(a_n=4n+7\)
C \(a_n=7n+4\)
D \(a_n=3n+7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7n-3\)
Step 1
Concept
The first term is (4) and (d=7), so (a_n=4+(n-1)7=7n-3). You can also check an option by putting (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=7n-3\). The first term is (4) and (d=7), so (a_n=4+(n-1)7=7n-3). You can also check an option by putting (n=1).
Step 3
Exam Tip
पहला पद (4) और (d=7) है इसलिए (a_n=4+(n-1)7=7n-3)। विकल्प को (n=1) रखकर भी जांच सकते हैं।
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यदि समानांतर श्रेढ़ी में \(a_3=19\) और \(a_6=34\) है, तो समान अंतर क्या है?
If an arithmetic progression has \(a_3=19\) and \(a_6=34\), what is the common difference?
#sequences
#progressions
#arithmetic-progression
#common-difference
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From the third to the sixth term there are (3) gaps and the increase is (15), so (d=5). Count the number of gaps correctly.
Step 2
Why this answer is correct
The correct answer is C. (5). From the third to the sixth term there are (3) gaps and the increase is (15), so (d=5). Count the number of gaps correctly.
Step 3
Exam Tip
तीसरे से छठे पद तक (3) अंतर हैं और वृद्धि (15) है, इसलिए (d=5)। अंतरालों की संख्या सही गिनें।
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यदि \(a_n=5n+6\) है, तो \(a_3+a_5\) कितना होगा?
If \(a_n=5n+6\), what is \(a_3+a_5\)?
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#progressions
#arithmetic-progression
#sum-of-terms
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A (42)
B (46)
C (48)
D (52)
Explanation opens after your attempt
Step 1
Concept
\(a_3=21\) and \(a_5=31\), so the sum is (52). Find both terms separately before adding.
Step 2
Why this answer is correct
The correct answer is D. (52). \(a_3=21\) and \(a_5=31\), so the sum is (52). Find both terms separately before adding.
Step 3
Exam Tip
\(a_3=21\) और \(a_5=31\), इसलिए योग (52) है। जोड़ने से पहले दोनों पद अलग निकालें।
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समानांतर श्रेढ़ी \(70,62,54,46,\ldots\) में (14) कौन-सा पद है?
In the arithmetic progression \(70,62,54,46,\ldots\), which term is (14)?
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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 (70+(n-1)(-8)=14), (n=8). The same \(a_n\) formula works in a decreasing progression.
Step 2
Why this answer is correct
The correct answer is B. (8)वाँ / (8)th. From (70+(n-1)(-8)=14), (n=8). The same \(a_n\) formula works in a decreasing progression.
Step 3
Exam Tip
(70+(n-1)(-8)=14) से (n=8) मिलता है। घटती श्रेढ़ी में भी वही \(a_n\) सूत्र लगता है।
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यदि समानांतर श्रेढ़ी का (5)वाँ पद (27) और समान अंतर (3) है, तो पहला पद क्या है?
If the (5)th term of an arithmetic progression is (27) and the common difference is (3), what is the first term?
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A (12)
B (15)
C (18)
D (21)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a+4d\), so (27=a+12) and (a=15). To move backward from a given term subtract common differences.
Step 2
Why this answer is correct
The correct answer is B. (15). \(a_5=a+4d\), so (27=a+12) and (a=15). To move backward from a given term subtract common differences.
Step 3
Exam Tip
\(a_5=a+4d\) इसलिए (27=a+12) और (a=15)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं।
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समानांतर श्रेढ़ी \(3,3,3,3,\ldots\) का समान अंतर क्या है?
What is the common difference of the arithmetic progression \(3,3,3,3,\ldots\)?
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A (0)
B (1)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Every consecutive difference is (3-3=0). A constant sequence is also an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. (0). Every consecutive difference is (3-3=0). A constant sequence is also an arithmetic progression.
Step 3
Exam Tip
हर लगातार अंतर (3-3=0) है। स्थिर अनुक्रम भी समानांतर श्रेढ़ी होता है।
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यदि (a=10) और (d=2) है, तो पहले (6) पदों का योग क्या होगा?
If (a=10) and (d=2), what will be the sum of the first (6) terms?
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#progressions
#arithmetic-progression
#sum
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A (80)
B (84)
C (90)
D (96)
Explanation opens after your attempt
Step 1
Concept
The first (6) terms are (10,12,14,16,18,20), and their sum is (90). For small (n), writing and adding terms is easy.
Step 2
Why this answer is correct
The correct answer is C. (90). The first (6) terms are (10,12,14,16,18,20), and their sum is (90). For small (n), writing and adding terms is easy.
Step 3
Exam Tip
पहले (6) पद (10,12,14,16,18,20) हैं और योग (90) है। छोटे (n) में पद लिखकर जोड़ना आसान है।
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समानांतर श्रेढ़ी \(19,23,27,31,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the arithmetic progression \(19,23,27,31,\ldots\)?
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#progressions
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#general-term
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A \(a_n=4n+19\)
B \(a_n=4n+15\)
C \(a_n=19n+4\)
D \(a_n=15n+4\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n+15\)
Step 1
Concept
The first term is (19) and (d=4), so (a_n=19+(n-1)4=4n+15). Remember (n-1) while forming the general term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n+15\). The first term is (19) and (d=4), so (a_n=19+(n-1)4=4n+15). Remember (n-1) while forming the general term.
Step 3
Exam Tip
पहला पद (19) और (d=4) है इसलिए (a_n=19+(n-1)4=4n+15)। सामान्य पद बनाते समय (n-1) का ध्यान रखें।
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यदि किसी समानांतर श्रेढ़ी में \(a_4=22\) और (d=6) है, तो \(a_9\) क्या होगा?
If an arithmetic progression has \(a_4=22\) and (d=6), what will be \(a_9\)?
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#term-relation
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A (46)
B (48)
C (50)
D (52)
Explanation opens after your attempt
Step 1
Concept
From \(a_4\) to \(a_9\), there are (5) gaps, so (a_9=22+5(6)=52). Moving forward from a nearby term is a quick method.
Step 2
Why this answer is correct
The correct answer is D. (52). From \(a_4\) to \(a_9\), there are (5) gaps, so (a_9=22+5(6)=52). Moving forward from a nearby term is a quick method.
Step 3
Exam Tip
\(a_4\) से \(a_9\) तक (5) अंतर हैं, इसलिए (a_9=22+5(6)=52)। पास के पद से आगे बढ़ना तेज तरीका है।
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किस विकल्प में (a=13) और (d=5) वाली समानांतर श्रेढ़ी के पहले चार पद हैं?
Which option has the first four terms of the arithmetic progression with (a=13) and (d=5)?
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#progressions
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#sequence-formation
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A (13,18,23,28)
B (13,17,21,25)
C (5,13,21,29)
D (18,23,28,33)
Explanation opens after your attempt
Correct Answer
A. (13,18,23,28)
Step 1
Concept
The first term is (13), and adding (5) each time gives (13,18,23,28). Form the terms directly from the given (a) and (d).
Step 2
Why this answer is correct
The correct answer is A. (13,18,23,28). The first term is (13), and adding (5) each time gives (13,18,23,28). Form the terms directly from the given (a) and (d).
Step 3
Exam Tip
पहला पद (13) है और हर बार (5) जोड़ने पर (13,18,23,28) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं।
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यदि समानांतर श्रेढ़ी के लगातार तीन पद (x), (x+6), (2x) हैं, तो (x) का मान क्या है?
If three consecutive terms of an arithmetic progression are (x), (x+6), (2x), what is the value of (x)?
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A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
In an arithmetic progression (2(x+6)=x+2x), so (x=12). The middle term is the average of the two surrounding terms.
Step 2
Why this answer is correct
The correct answer is D. (12). In an arithmetic progression (2(x+6)=x+2x), so (x=12). The middle term is the average of the two surrounding terms.
Step 3
Exam Tip
समानांतर श्रेढ़ी में (2(x+6)=x+2x), इसलिए (x=12)। बीच का पद दोनों ओर के पदों का औसत होता है।
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समानांतर श्रेढ़ी \(45,39,33,27,\ldots\) का पहला ऋणात्मक पद कौन-सा है?
What is the first negative term of the arithmetic progression \(45,39,33,27,\ldots\)?
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#negative-term
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
Explanation opens after your attempt
Correct Answer
B. (9)वाँ / (9)th
Step 1
Concept
\(a_8=3\) and \(a_9=-3\), so the first negative term is the (9)th. Check the first term that goes below zero.
Step 2
Why this answer is correct
The correct answer is B. (9)वाँ / (9)th. \(a_8=3\) and \(a_9=-3\), so the first negative term is the (9)th. Check the first term that goes below zero.
Step 3
Exam Tip
\(a_8=3\) और \(a_9=-3\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद जांचें।
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यदि \(a_n=11-2n\) है, तो इस समानांतर श्रेढ़ी का तीसरा पद क्या है?
If \(a_n=11-2n\), what is the third term of this arithmetic progression?
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#nth-term
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
(a_3=11-2(3)=5). Substitute (n=3) directly in the given rule.
Step 2
Why this answer is correct
The correct answer is B. (5). (a_3=11-2(3)=5). Substitute (n=3) directly in the given rule.
Step 3
Exam Tip
(a_3=11-2(3)=5)। दिए नियम में सीधे (n=3) रखें।
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समानांतर श्रेढ़ी \(6,14,22,30,\ldots\) के पहले (3) पदों का औसत क्या है?
What is the average of the first (3) terms of the arithmetic progression \(6,14,22,30,\ldots\)?
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#average
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A (12)
B (14)
C (16)
D (18)
Explanation opens after your attempt
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is B. (14). 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.
Step 3
Exam Tip
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।
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यदि \(a_1=5\) और \(a_{10}=50\) है, तो समान अंतर क्या होगा?
If \(a_1=5\) and \(a_{10}=50\), what will be the common difference?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From \(a_{10}=5+9d=50\), (9d=45) and (d=5). Up to the (10)th term there are (9) gaps.
Step 2
Why this answer is correct
The correct answer is B. (5). From \(a_{10}=5+9d=50\), (9d=45) and (d=5). Up to the (10)th term there are (9) gaps.
Step 3
Exam Tip
\(a_{10}=5+9d=50\) से (9d=45) और (d=5)। (10)वें पद तक (9) अंतर होते हैं।
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समानांतर श्रेढ़ी \(2,10,18,26,\ldots\) का (15)वाँ पद क्या है?
What is the (15)th term of the arithmetic progression \(2,10,18,26,\ldots\)?
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A (106)
B (110)
C (114)
D (118)
Explanation opens after your attempt
Step 1
Concept
Here (a=2) and (d=8), so (a_{15}=2+14(8)=114). Use the same formula even for a larger term.
Step 2
Why this answer is correct
The correct answer is C. (114). Here (a=2) and (d=8), so (a_{15}=2+14(8)=114). Use the same formula even for a larger term.
Step 3
Exam Tip
यहाँ (a=2) और (d=8), इसलिए (a_{15}=2+14(8)=114)। बड़े पद के लिए भी वही सूत्र लगाएं।
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किस समानांतर श्रेढ़ी का समान अंतर (9) है?
Which arithmetic progression has common difference (9)?
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A \(9,18,27,36,\ldots\)
B \(18,9,0,-9,\ldots\)
C \(3,9,27,81,\ldots\)
D \(1,9,18,28,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(9,18,27,36,\ldots\)
Step 1
Concept
In \(9,18,27,36,\ldots\), (9) is added each time. To find the common difference check the difference of two consecutive terms.
Step 2
Why this answer is correct
The correct answer is A. \(9,18,27,36,\ldots\). In \(9,18,27,36,\ldots\), (9) is added each time. To find the common difference check the difference of two consecutive terms.
Step 3
Exam Tip
\(9,18,27,36,\ldots\) में हर बार (9) जुड़ता है। समान अंतर निकालने में लगातार दो पदों का अंतर देखें।
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यदि \(a_n=6n+1\) है, तो \(a_n=49\) किस पद पर होगा?
If \(a_n=6n+1\), at which term will \(a_n=49\)?
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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
From (6n+1=49), (6n=48) and (n=8). To find the position set \(a_n\) equal to the given value.
Step 2
Why this answer is correct
The correct answer is C. (8)वाँ / (8)th. From (6n+1=49), (6n=48) and (n=8). To find the position set \(a_n\) equal to the given value.
Step 3
Exam Tip
(6n+1=49) से (6n=48) और (n=8)। पद का स्थान निकालने के लिए \(a_n\) को दिए मान के बराबर रखें।
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समानांतर श्रेढ़ी \(30,25,20,15,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of the arithmetic progression \(30,25,20,15,\ldots\)?
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#sum
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A (90)
B (100)
C (110)
D (120)
Explanation opens after your attempt
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is B. (100). 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.
Step 3
Exam Tip
पहले (5) पद (30,25,20,15,10) हैं और योग (100) है। घटती श्रेढ़ी में भी पद क्रम से लिखकर जोड़ें।
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यदि समानांतर श्रेढ़ी में \(a_6=41\) और (d=7) है, तो \(a_3\) क्या होगा?
If an arithmetic progression has \(a_6=41\) and (d=7), what is \(a_3\)?
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A (17)
B (20)
C (23)
D (26)
Explanation opens after your attempt
Step 1
Concept
From \(a_6\) to \(a_3\), move back (3) gaps, so (a_3=41-3(7)=20). When moving backward subtract the common difference.
Step 2
Why this answer is correct
The correct answer is B. (20). From \(a_6\) to \(a_3\), move back (3) gaps, so (a_3=41-3(7)=20). When moving backward subtract the common difference.
Step 3
Exam Tip
\(a_6\) से \(a_3\) तक (3) अंतर पीछे जाना है, इसलिए (a_3=41-3(7)=20)। पीछे जाते समय समान अंतर घटाएं।
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समानांतर श्रेढ़ी \(24,18,12,6,\ldots\) में (0) कौन-सा पद है?
In the arithmetic progression \(24,18,12,6,\ldots\), which term is (0)?
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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
B. (5)वाँ / (5)th
Step 1
Concept
From (24+(n-1)(-6)=0), (n=5). Zero can also be a term of a progression.
Step 2
Why this answer is correct
The correct answer is B. (5)वाँ / (5)th. From (24+(n-1)(-6)=0), (n=5). Zero can also be a term of a progression.
Step 3
Exam Tip
(24+(n-1)(-6)=0) से (n=5) मिलता है। शून्य भी श्रेढ़ी का पद हो सकता है।
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यदि (a=17) और (d=0) है, तो (10)वाँ पद क्या होगा?
If (a=17) and (d=0), what will be the (10)th term?
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A (0)
B (10)
C (17)
D (170)
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Step 1
Concept
When (d=0), every term remains (17). In a constant arithmetic progression all terms are equal.
Step 2
Why this answer is correct
The correct answer is C. (17). When (d=0), every term remains (17). In a constant arithmetic progression all terms are equal.
Step 3
Exam Tip
(d=0) होने पर हर पद (17) ही रहेगा। स्थिर समानांतर श्रेढ़ी में सभी पद बराबर होते हैं।
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समानांतर श्रेढ़ी \(1,7,13,19,\ldots\) में \(a_{11}-a_5\) का मान क्या है?
In the arithmetic progression \(1,7,13,19,\ldots\), what is the value of \(a_{11}-a_5\)?
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#progressions
#arithmetic-progression
#difference-of-terms
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A (24)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
There are (6) gaps between \(a_{11}\) and \(a_5\), and (d=6), so the difference is (36). In an arithmetic progression term difference depends on the difference of positions.
Step 2
Why this answer is correct
The correct answer is C. (36). There are (6) gaps between \(a_{11}\) and \(a_5\), and (d=6), so the difference is (36). In an arithmetic progression term difference depends on the difference of positions.
Step 3
Exam Tip
\(a_{11}\) और \(a_5\) के बीच (6) अंतर हैं और (d=6), इसलिए अंतर (36) है। समानांतर श्रेढ़ी में पदों का अंतर पद-संख्या के अंतर पर निर्भर करता है।
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किस विकल्प में \(a_n=10-3n\) से बने पहले चार पद हैं?
Which option has the first four terms formed by \(a_n=10-3n\)?
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#arithmetic-progression
#sequence-from-rule
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A (7,4,1,-2)
B (10,7,4,1)
C (13,10,7,4)
D (3,6,9,12)
Explanation opens after your attempt
Correct Answer
A. (7,4,1,-2)
Step 1
Concept
Putting (n=1,2,3,4) gives (7,4,1,-2). When forming terms from a rule start with (n=1).
Step 2
Why this answer is correct
The correct answer is A. (7,4,1,-2). Putting (n=1,2,3,4) gives (7,4,1,-2). When forming terms from a rule start with (n=1).
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (7,4,1,-2) मिलते हैं। नियम से पद बनाते समय (n=1) से शुरू करें।
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समानांतर श्रेढ़ी \(10,16,22,28,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of the arithmetic progression \(10,16,22,28,\ldots\)?
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#progressions
#arithmetic-progression
#sum
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A (140)
B (145)
C (150)
D (155)
Explanation opens after your attempt
Step 1
Concept
The first (6) terms are (10,16,22,28,34,40), and their sum is (150). Write the terms in correct order and add.
Step 2
Why this answer is correct
The correct answer is C. (150). The first (6) terms are (10,16,22,28,34,40), and their sum is (150). Write the terms in correct order and add.
Step 3
Exam Tip
पहले (6) पद (10,16,22,28,34,40) हैं और योग (150) है। पद सही क्रम में लिखकर जोड़ें।
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यदि समानांतर श्रेढ़ी में \(a_2=9\) और \(a_8=39\) है, तो \(a_5\) क्या होगा?
If an arithmetic progression has \(a_2=9\) and \(a_8=39\), what is \(a_5\)?
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#progressions
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#term-relation
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A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
From \(a_2\) to \(a_8\), the increase over (6) gaps is (30), so (d=5), hence (a_5=9+3(5)=24). Find the common difference first.
Step 2
Why this answer is correct
The correct answer is C. (24). From \(a_2\) to \(a_8\), the increase over (6) gaps is (30), so (d=5), hence (a_5=9+3(5)=24). Find the common difference first.
Step 3
Exam Tip
\(a_2\) से \(a_8\) तक (6) अंतर में वृद्धि (30) है इसलिए (d=5), अतः (a_5=9+3(5)=24)। पहले समान अंतर निकालें।
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समानांतर श्रेढ़ी \(6,10,14,\ldots\) में अगले दो पद कौन-से हैं?
In the arithmetic progression \(6,10,14,\ldots\), what are the next two terms?
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#next-terms
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A (16,18)
B (18,22)
C (20,24)
D (22,26)
Explanation opens after your attempt
Correct Answer
B. (18,22)
Step 1
Concept
The common difference is (4), so after (14) the next terms are (18) and (22). Keep adding the common difference for next terms.
Step 2
Why this answer is correct
The correct answer is B. (18,22). The common difference is (4), so after (14) the next terms are (18) and (22). Keep adding the common difference for next terms.
Step 3
Exam Tip
समान अंतर (4) है इसलिए (14) के बाद (18) और (22) आएंगे। अगले पदों के लिए समान अंतर जोड़ते रहें।
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यदि (a=3) और (d=11) है, तो \(a_6-a_2\) क्या होगा?
If (a=3) and (d=11), what will \(a_6-a_2\) be?
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#arithmetic-progression
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A (33)
B (44)
C (55)
D (66)
Explanation opens after your attempt
Step 1
Concept
There are (4) gaps between \(a_6\) and \(a_2\), so the difference is \(4\times11=44\). For term difference look at the difference of positions.
Step 2
Why this answer is correct
The correct answer is B. (44). There are (4) gaps between \(a_6\) and \(a_2\), so the difference is \(4\times11=44\). For term difference look at the difference of positions.
Step 3
Exam Tip
\(a_6\) और \(a_2\) के बीच (4) अंतर हैं इसलिए अंतर \(4\times11=44\) है। पदों के अंतर के लिए पद-संख्या का अंतर देखें।
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समानांतर श्रेढ़ी \(27,30,33,36,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the arithmetic progression \(27,30,33,36,\ldots\)?
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#general-term
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A \(a_n=3n+24\)
B \(a_n=27n+3\)
C \(a_n=3n+27\)
D \(a_n=24n+3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n+24\)
Step 1
Concept
The first term is (27) and (d=3), so (a_n=27+(n-1)3=3n+24). Put (n=1) to check an option.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n+24\). The first term is (27) and (d=3), so (a_n=27+(n-1)3=3n+24). Put (n=1) to check an option.
Step 3
Exam Tip
पहला पद (27) और (d=3) है इसलिए (a_n=27+(n-1)3=3n+24)। विकल्प की जांच के लिए (n=1) रखें।
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समानांतर श्रेढ़ी \(32,27,22,17,\ldots\) में पहला ऋणात्मक पद कौन-सा है?
What is the first negative term in the arithmetic progression \(32,27,22,17,\ldots\)?
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#negative-term
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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
\(a_7=2\) and \(a_8=-3\), so the first negative term is the (8)th. Check carefully for the first term that goes below zero.
Step 2
Why this answer is correct
The correct answer is B. (8)वाँ / (8)th. \(a_7=2\) and \(a_8=-3\), so the first negative term is the (8)th. Check carefully for the first term that goes below zero.
Step 3
Exam Tip
\(a_7=2\) और \(a_8=-3\), इसलिए पहला ऋणात्मक पद (8)वाँ है। शून्य से नीचे जाने वाला पहला पद ध्यान से जांचें।
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