श्रेणी \(14,22,30,38,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(14,22,30,38,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (8n+14)
B (6n+8)
C (8n+6)
D (14n-8)
Explanation opens after your attempt
Step 1
Concept
The first term is (14) and the difference is (8), so (a_n=14+(n-1)8=8n+6). In an arithmetic sequence, (n-1) differences are added.
Step 2
Why this answer is correct
The correct answer is C. (8n+6). The first term is (14) and the difference is (8), so (a_n=14+(n-1)8=8n+6). In an arithmetic sequence, (n-1) differences are added.
Step 3
Exam Tip
पहला पद (14) और अंतर (8) है इसलिए (a_n=14+(n-1)8=8n+6)। समान्तर श्रेणी में (n-1) अंतर जुड़ते हैं।
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यदि \(a_n=5n^2-4n+3\), तो \(a_6\) का मान क्या होगा?
If \(a_n=5n^2-4n+3\), what is the value of \(a_6\)?
#sequences
#progressions
#nth-term
#quadratic
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A (153)
B (159)
C (165)
D (151)
Explanation opens after your attempt
Step 1
Concept
Putting (n=6), (5(6)2 -4(6)+3=159). Calculate \(n^2\) first in a squared term.
Step 2
Why this answer is correct
The correct answer is B. (159). Putting (n=6), (5(6)2 -4(6)+3=159). Calculate \(n^2\) first in a squared term.
Step 3
Exam Tip
(n=6) रखने पर (5(6)2 -4(6)+3=159)। वर्ग वाले पद में पहले \(n^2\) निकालें।
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किसी समान्तर श्रेणी में \(a_4=21\) और \(a_{10}=57\) है। उसका (n)वां पद क्या होगा?
In an arithmetic sequence, \(a_4=21\) and \(a_{10}=57\). What is its (n)th term?
#sequences
#progressions
#nth-term
#arithmetic
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A (6n-3)
B (6n+3)
C (5n+1)
D (7n-7)
Explanation opens after your attempt
Step 1
Concept
From (6d=36), (d=6) and \(a_1=3\), so \(a_n=6n-3\). When two terms are given, find the common difference first.
Step 2
Why this answer is correct
The correct answer is A. (6n-3). From (6d=36), (d=6) and \(a_1=3\), so \(a_n=6n-3\). When two terms are given, find the common difference first.
Step 3
Exam Tip
(6d=36) से (d=6) और \(a_1=3\), इसलिए \(a_n=6n-3\)। दो पद दिए हों तो पहले सामान्य अंतर निकालें।
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श्रेणी \(7,18,33,52,75,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(7,18,33,52,75,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(n^2+6n\)
B \(2n^2+5n\)
C \(2n^2+4n+1\)
D \(3n^2+n+3\)
Explanation opens after your attempt
Correct Answer
B. \(2n^2+5n\)
Step 1
Concept
The given terms match \(2n^2+5n\). In a quadratic pattern, test the options on the first three terms.
Step 2
Why this answer is correct
The correct answer is B. \(2n^2+5n\). The given terms match \(2n^2+5n\). In a quadratic pattern, test the options on the first three terms.
Step 3
Exam Tip
दिए गए पद \(2n^2+5n\) से मिलते हैं। द्विघात पैटर्न में पहले तीन पदों पर विकल्प जांचें।
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यदि \(a_n=9n-11\), तो \(a_{2k+3}\) किसके बराबर होगा?
If \(a_n=9n-11\), what is \(a_{2k+3}\)?
#sequences
#progressions
#nth-term
#algebra
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A (18k+16)
B (18k+27)
C (9k+16)
D (18k-11)
Explanation opens after your attempt
Correct Answer
A. (18k+16)
Step 1
Concept
Putting (n=2k+3), (a_{2k+3}=9(2k+3)-11=18k+16). Substitute the whole expression used as the index.
Step 2
Why this answer is correct
The correct answer is A. (18k+16). Putting (n=2k+3), (a_{2k+3}=9(2k+3)-11=18k+16). Substitute the whole expression used as the index.
Step 3
Exam Tip
(n=2k+3) रखने पर (a_{2k+3}=9(2k+3)-11=18k+16)। सूचकांक का पूरा व्यंजक प्रतिस्थापित करें।
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श्रेणी \(4,20,100,500,\ldots\) का (7)वां पद क्या होगा?
What is the (7)th term of the sequence \(4,20,100,500,\ldots\)?
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#nth-term
#geometric
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A (31250)
B (15625)
C (62500)
D (125000)
Explanation opens after your attempt
Correct Answer
C. (62500)
Step 1
Concept
This is a geometric sequence and \(a_7=4\cdot5^6=62500\). In a geometric sequence, the exponent is (n-1).
Step 2
Why this answer is correct
The correct answer is C. (62500). This is a geometric sequence and \(a_7=4\cdot5^6=62500\). In a geometric sequence, the exponent is (n-1).
Step 3
Exam Tip
यह गुणोत्तर श्रेणी है और \(a_7=4\cdot5^6=62500\)। गुणोत्तर श्रेणी में घात (n-1) होती है।
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यदि \(a_n=n^2+7n-8\), तो \(a_9-a_4\) का मान क्या है?
If \(a_n=n^2+7n-8\), what is the value of \(a_9-a_4\)?
#sequences
#progressions
#nth-term
#quadratic
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A (96)
B (100)
C (104)
D (108)
Explanation opens after your attempt
Step 1
Concept
\(a_9=136\) and \(a_4=36\), so the difference is (100). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (100). \(a_9=136\) and \(a_4=36\), so the difference is (100). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_9=136\) और \(a_4=36\), इसलिए अंतर (100) है। दोनों पद अलग निकालकर घटाएं।
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श्रेणी \(3,11,23,39,59,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(3,11,23,39,59,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(2n^2+2n-1\)
B \(n^2+4n-2\)
C \(2n^2+n\)
D \(3n^2-1\)
Explanation opens after your attempt
Correct Answer
A. \(2n^2+2n-1\)
Step 1
Concept
The terms match \(2n^2+2n-1\). If second differences are equal, look for a quadratic rule.
Step 2
Why this answer is correct
The correct answer is A. \(2n^2+2n-1\). The terms match \(2n^2+2n-1\). If second differences are equal, look for a quadratic rule.
Step 3
Exam Tip
पद \(2n^2+2n-1\) से मिलते हैं। दूसरे अंतर समान हों तो द्विघात नियम खोजें।
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यदि \(a_n=26-5n\), तो कौन सा पद (-34) के बराबर है?
If \(a_n=26-5n\), which term is equal to (-34)?
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#nth-term
#equation
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A (10)वां / (10)th
B (11)वां / (11)th
C (12)वां / (12)th
D (13)वां / (13)th
Explanation opens after your attempt
Correct Answer
C. (12)वां / (12)th
Step 1
Concept
From (26-5n=-34), (5n=60), so (n=12). Be careful with signs in negative terms.
Step 2
Why this answer is correct
The correct answer is C. (12)वां / (12)th. From (26-5n=-34), (5n=60), so (n=12). Be careful with signs in negative terms.
Step 3
Exam Tip
(26-5n=-34) से (5n=60), इसलिए (n=12)। ऋणात्मक पदों में चिन्हों पर ध्यान दें।
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श्रेणी \(6,14,24,36,50,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(6,14,24,36,50,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(n^2+5n\)
B \(2n^2+4\)
C \(n^2+4n+1\)
D \(3n^2+3n\)
Explanation opens after your attempt
Correct Answer
A. \(n^2+5n\)
Step 1
Concept
The terms match \(n^2+5n\), giving (6) for (n=1) and (14) for (n=2). Test options on the starting terms.
Step 2
Why this answer is correct
The correct answer is A. \(n^2+5n\). The terms match \(n^2+5n\), giving (6) for (n=1) and (14) for (n=2). Test options on the starting terms.
Step 3
Exam Tip
पद \(n^2+5n\) से मिलते हैं क्योंकि (n=1) पर (6) और (n=2) पर (14) आता है। विकल्पों को शुरुआती पदों पर जांचें।
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यदि (a_n=(-1)^{n+1}(4n+1)), तो \(a_8\) का मान क्या होगा?
If (a_n=(-1)^{n+1}(4n+1)), what is the value of \(a_8\)?
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#progressions
#nth-term
#alternating
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A (33)
B (-33)
C (31)
D (-31)
Explanation opens after your attempt
Step 1
Concept
For (n=8), ((-1)9 =-1) and (4(8)+1=33), so \(a_8=-33\). In alternating signs, check whether the exponent is even or odd.
Step 2
Why this answer is correct
The correct answer is B. (-33). For (n=8), ((-1)9 =-1) and (4(8)+1=33), so \(a_8=-33\). In alternating signs, check whether the exponent is even or odd.
Step 3
Exam Tip
(n=8) पर ((-1)9 =-1) और (4(8)+1=33), इसलिए \(a_8=-33\)। वैकल्पिक चिन्ह में घात की सम-विषम स्थिति देखें।
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किसी समान्तर श्रेणी में \(a_7=38\) और सामान्य अंतर (6) है। उसका (n)वां पद क्या होगा?
In an arithmetic sequence, \(a_7=38\) and the common difference is (6). What is its (n)th term?
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#progressions
#nth-term
#arithmetic
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A (6n+2)
B (6n-4)
C (6n+8)
D (7n-4)
Explanation opens after your attempt
Step 1
Concept
From \(a_7=a_1+6d\), \(a_1=2\), so (a_n=2+(n-1)6=6n-4). Finding the first term from a middle term is useful.
Step 2
Why this answer is correct
The correct answer is B. (6n-4). From \(a_7=a_1+6d\), \(a_1=2\), so (a_n=2+(n-1)6=6n-4). Finding the first term from a middle term is useful.
Step 3
Exam Tip
\(a_7=a_1+6d\) से \(a_1=2\), इसलिए (a_n=2+(n-1)6=6n-4)। मध्य पद से पहला पद निकालना उपयोगी है।
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श्रेणी \(10,18,34,66,130,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(10,18,34,66,130,\ldots\)?
#sequences
#progressions
#nth-term
#exponential
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A \(2^{n+2}+2\)
B \(2^{n+1}+6\)
C \(2^n+8\)
D (4n+6)
Explanation opens after your attempt
Correct Answer
A. \(2^{n+2}+2\)
Step 1
Concept
The terms are \(8+2,16+2,32+2,\ldots\), so \(a_n=2^{n+2}+2\). In exponential patterns, identify the starting power.
Step 2
Why this answer is correct
The correct answer is A. \(2^{n+2}+2\). The terms are \(8+2,16+2,32+2,\ldots\), so \(a_n=2^{n+2}+2\). In exponential patterns, identify the starting power.
Step 3
Exam Tip
पद \(8+2,16+2,32+2,\ldots\) हैं इसलिए \(a_n=2^{n+2}+2\)। घातीय पैटर्न में शुरुआती घात पहचानें।
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श्रेणी \(\frac{7}{4},\frac{7}{2},\frac{21}{4},7,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(\frac{7}{4},\frac{7}{2},\frac{21}{4},7,\ldots\)?
#sequences
#progressions
#nth-term
#fractions
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A (\frac{7(n+1)}{4})
B \(\frac{7n}{4}\)
C \(\frac{4n}{7}\)
D (7n)
Explanation opens after your attempt
Correct Answer
B. \(\frac{7n}{4}\)
Step 1
Concept
Each term increases by \(\frac{7}{4}\), so \(a_n=\frac{7n}{4}\). Use a common denominator to see the pattern in fractions.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7n}{4}\). Each term increases by \(\frac{7}{4}\), so \(a_n=\frac{7n}{4}\). Use a common denominator to see the pattern in fractions.
Step 3
Exam Tip
हर पद में \(\frac{7}{4}\) की वृद्धि है इसलिए \(a_n=\frac{7n}{4}\)। भिन्नों में समान हर बनाकर पैटर्न देखें।
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श्रेणी \(4,13,28,49,76,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(4,13,28,49,76,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(2n^2+n+1\)
B \(3n^2+1\)
C \(n^2+6n-3\)
D \(3n^2+n\)
Explanation opens after your attempt
Correct Answer
B. \(3n^2+1\)
Step 1
Concept
The given terms match \(3n^2+1\). When the second difference is (6), the coefficient of \(n^2\) is (3).
Step 2
Why this answer is correct
The correct answer is B. \(3n^2+1\). The given terms match \(3n^2+1\). When the second difference is (6), the coefficient of \(n^2\) is (3).
Step 3
Exam Tip
दिए गए पद \(3n^2+1\) से मिलते हैं। दूसरे अंतर (6) होने पर \(n^2\) का गुणांक (3) होता है।
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यदि \(a_n=6n^2-5n+2\), तो \(a_{n+1}-a_n\) क्या होगा?
If \(a_n=6n^2-5n+2\), what is \(a_{n+1}-a_n\)?
#sequences
#progressions
#nth-term
#algebra
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A (12n-5)
B (12n+1)
C (6n+7)
D (12n+7)
Explanation opens after your attempt
Correct Answer
B. (12n+1)
Step 1
Concept
\(a_{n+1}=6n^2+7n+3\), so the difference is (12n+1). Expand ((n+1)2 ) carefully.
Step 2
Why this answer is correct
The correct answer is B. (12n+1). \(a_{n+1}=6n^2+7n+3\), so the difference is (12n+1). Expand ((n+1)2 ) carefully.
Step 3
Exam Tip
\(a_{n+1}=6n^2+7n+3\), इसलिए अंतर (12n+1) है। (n+1) का वर्ग सावधानी से खोलें।
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किसी श्रेणी का \(a_n=n^3+2n\) है। \(a_5\) का मान क्या है?
A sequence has \(a_n=n^3+2n\). What is the value of \(a_5\)?
#sequences
#progressions
#nth-term
#cubic
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A (125)
B (130)
C (135)
D (140)
Explanation opens after your attempt
Step 1
Concept
(a_5=53 +2(5)=135). Calculate the cubic and linear parts separately.
Step 2
Why this answer is correct
The correct answer is C. (135). (a_5=53 +2(5)=135). Calculate the cubic and linear parts separately.
Step 3
Exam Tip
(a_5=53 +2(5)=135)। घन और रैखिक भाग अलग-अलग निकालें।
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श्रेणी \(31,26,21,16,11,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(31,26,21,16,11,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (31-5n)
B (36-5n)
C (5n+26)
D (35-4n)
Explanation opens after your attempt
Correct Answer
B. (36-5n)
Step 1
Concept
The first term is (31) and the difference is (-5), so (a_n=31+(n-1)(-5)=36-5n). Use a negative difference in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. (36-5n). The first term is (31) and the difference is (-5), so (a_n=31+(n-1)(-5)=36-5n). Use a negative difference in a decreasing sequence.
Step 3
Exam Tip
पहला पद (31) और अंतर (-5) है इसलिए (a_n=31+(n-1)(-5)=36-5n)। घटती श्रेणी में अंतर ऋणात्मक लें।
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यदि \(a_n=3^n+2n\), तो \(a_4\) का मान क्या होगा?
If \(a_n=3^n+2n\), what is the value of \(a_4\)?
#sequences
#progressions
#nth-term
#exponential
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A (83)
B (87)
C (89)
D (91)
Explanation opens after your attempt
Step 1
Concept
(a_4=34 +2(4)=81+8=89). Calculate the power and the linear part separately.
Step 2
Why this answer is correct
The correct answer is C. (89). (a_4=34 +2(4)=81+8=89). Calculate the power and the linear part separately.
Step 3
Exam Tip
(a_4=34 +2(4)=81+8=89)। घात और रैखिक भाग को अलग निकालें।
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श्रेणी \(15,27,41,57,75,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(15,27,41,57,75,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(n^2+9n+5\)
B \(2n^2+7n+6\)
C \(n^2+8n+6\)
D \(3n^2+6n+6\)
Explanation opens after your attempt
Correct Answer
A. \(n^2+9n+5\)
Step 1
Concept
The terms match \(n^2+9n+5\). Options should be tested on the first two or three terms.
Step 2
Why this answer is correct
The correct answer is A. \(n^2+9n+5\). The terms match \(n^2+9n+5\). Options should be tested on the first two or three terms.
Step 3
Exam Tip
पद \(n^2+9n+5\) से मिलते हैं। विकल्पों को पहले दो या तीन पदों पर जांचना चाहिए।
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किसी समान्तर श्रेणी का (n)वां पद \(a_n=11n-17\) है। कौन सा पद (159) है?
The (n)th term of an arithmetic sequence is \(a_n=11n-17\). Which term is (159)?
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#progressions
#nth-term
#equation
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A (14)वां / (14)th
B (15)वां / (15)th
C (16)वां / (16)th
D (17)वां / (17)th
Explanation opens after your attempt
Correct Answer
C. (16)वां / (16)th
Step 1
Concept
From (11n-17=159), (11n=176), so (n=16). Form an equation to find the term number.
Step 2
Why this answer is correct
The correct answer is C. (16)वां / (16)th. From (11n-17=159), (11n=176), so (n=16). Form an equation to find the term number.
Step 3
Exam Tip
(11n-17=159) से (11n=176), इसलिए (n=16)। पद संख्या निकालने के लिए समीकरण बनाएं।
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श्रेणी \(\frac{9}{5},\frac{18}{5},\frac{27}{5},\frac{36}{5},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(\frac{9}{5},\frac{18}{5},\frac{27}{5},\frac{36}{5},\ldots\)?
#sequences
#progressions
#nth-term
#fractions
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A \(\frac{5n}{9}\)
B (\frac{9(n+1)}{5})
C \(\frac{9n}{5}\)
D (9n)
Explanation opens after your attempt
Correct Answer
C. \(\frac{9n}{5}\)
Step 1
Concept
Each term increases by \(\frac{9}{5}\), so \(a_n=\frac{9n}{5}\). In fractions with a common denominator, observe the numerator pattern.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{9n}{5}\). Each term increases by \(\frac{9}{5}\), so \(a_n=\frac{9n}{5}\). In fractions with a common denominator, observe the numerator pattern.
Step 3
Exam Tip
हर पद में \(\frac{9}{5}\) की वृद्धि है इसलिए \(a_n=\frac{9n}{5}\)। समान हर वाले भिन्नों में अंश का पैटर्न देखें।
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यदि \(a_n=2n^2+3n-4\), तो \(a_8-a_5\) का मान क्या है?
If \(a_n=2n^2+3n-4\), what is the value of \(a_8-a_5\)?
#sequences
#progressions
#nth-term
#quadratic
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A (81)
B (84)
C (87)
D (90)
Explanation opens after your attempt
Step 1
Concept
\(a_8=148\) and \(a_5=61\), so the difference is (87). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is C. (87). \(a_8=148\) and \(a_5=61\), so the difference is (87). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_8=148\) और \(a_5=61\), इसलिए अंतर (87) है। दोनों पद अलग निकालकर घटाएं।
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श्रेणी \(3,12,27,48,75,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(3,12,27,48,75,\ldots\)?
#sequences
#progressions
#nth-term
#squares
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A \(3n^2\)
B \(2n^2+n\)
C \(n^2+2n\)
D \(3n^2+3\)
Explanation opens after your attempt
Correct Answer
A. \(3n^2\)
Step 1
Concept
The terms are \(3\cdot1^2,3\cdot2^2,3\cdot3^2,\ldots\), so \(a_n=3n^2\). Recognize the square pattern with its coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(3n^2\). The terms are \(3\cdot1^2,3\cdot2^2,3\cdot3^2,\ldots\), so \(a_n=3n^2\). Recognize the square pattern with its coefficient.
Step 3
Exam Tip
पद \(3\cdot1^2,3\cdot2^2,3\cdot3^2,\ldots\) हैं इसलिए \(a_n=3n^2\)। गुणांक वाले वर्ग पैटर्न को पहचानें।
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यदि \(a_n=17-4n\), तो \(a_5+a_{11}\) का मान क्या है?
If \(a_n=17-4n\), what is the value of \(a_5+a_{11}\)?
#sequences
#progressions
#nth-term
#linear
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A (-28)
B (-30)
C (-32)
D (-34)
Explanation opens after your attempt
Step 1
Concept
\(a_5=-3\) and \(a_{11}=-27\), so the sum is (-30). Add negative numbers carefully.
Step 2
Why this answer is correct
The correct answer is B. (-30). \(a_5=-3\) and \(a_{11}=-27\), so the sum is (-30). Add negative numbers carefully.
Step 3
Exam Tip
\(a_5=-3\) और \(a_{11}=-27\), इसलिए योग (-30) है। ऋणात्मक संख्याओं का योग सावधानी से करें।
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श्रेणी \(27,64,125,216,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(27,64,125,216,\ldots\)?
#sequences
#progressions
#nth-term
#cubes
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A \(n^3+26\)
B ((n+1)3 )
C ((n+2)3 )
D \(3n^3\)
Explanation opens after your attempt
Correct Answer
C. ((n+2)3 )
Step 1
Concept
The terms are \(3^3,4^3,5^3,\ldots\), so (a_n=(n+2)3 ). In cube sequences, observe the starting base.
Step 2
Why this answer is correct
The correct answer is C. ((n+2)3 ). The terms are \(3^3,4^3,5^3,\ldots\), so (a_n=(n+2)3 ). In cube sequences, observe the starting base.
Step 3
Exam Tip
पद \(3^3,4^3,5^3,\ldots\) हैं इसलिए (a_n=(n+2)3 )। घन श्रेणी में शुरुआती आधार देखें।
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किसी श्रेणी का \(a_n=8n+3\) है। \(a_{n+5}-a_n\) का मान क्या होगा?
A sequence has \(a_n=8n+3\). What is the value of \(a_{n+5}-a_n\)?
#sequences
#progressions
#nth-term
#difference
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A (32)
B (35)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
The index increases by (5) and the common difference is (8), so the difference is (40). In a linear rule, the coefficient of (n) gives the common difference.
Step 2
Why this answer is correct
The correct answer is D. (40). The index increases by (5) and the common difference is (8), so the difference is (40). In a linear rule, the coefficient of (n) gives the common difference.
Step 3
Exam Tip
सूचकांक (5) बढ़ा है और सामान्य अंतर (8) है इसलिए अंतर (40) होगा। रैखिक नियम में (n) का गुणांक सामान्य अंतर देता है।
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श्रेणी \(5,15,45,135,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(5,15,45,135,\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A \(5\cdot3^{n-1}\)
B \(3\cdot5^{n-1}\)
C \(5\cdot3^n\)
D \(15\cdot3^{n-1}\)
Explanation opens after your attempt
Correct Answer
A. \(5\cdot3^{n-1}\)
Step 1
Concept
Each term is multiplied by (3), so \(a_n=5\cdot3^{n-1}\). In a geometric sequence, the first term stays separate.
Step 2
Why this answer is correct
The correct answer is A. \(5\cdot3^{n-1}\). Each term is multiplied by (3), so \(a_n=5\cdot3^{n-1}\). In a geometric sequence, the first term stays separate.
Step 3
Exam Tip
हर बार गुणन (3) हो रहा है इसलिए \(a_n=5\cdot3^{n-1}\)। गुणोत्तर श्रेणी में पहला पद अलग रहता है।
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यदि \(a_n=4n^2+n-6\), तो \(a_{n+2}-a_n\) क्या होगा?
If \(a_n=4n^2+n-6\), what is \(a_{n+2}-a_n\)?
#sequences
#progressions
#nth-term
#algebra
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A (8n+10)
B (16n+12)
C (16n+18)
D (12n+18)
Explanation opens after your attempt
Correct Answer
C. (16n+18)
Step 1
Concept
\(a_{n+2}=4n^2+17n+12\), so the difference is (16n+18). Expand ((n+2)2 ) correctly.
Step 2
Why this answer is correct
The correct answer is C. (16n+18). \(a_{n+2}=4n^2+17n+12\), so the difference is (16n+18). Expand ((n+2)2 ) correctly.
Step 3
Exam Tip
\(a_{n+2}=4n^2+17n+12\), इसलिए अंतर (16n+18) है। (n+2) का वर्ग सही खोलें।
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किसी समान्तर श्रेणी में \(a_5=32\) और \(a_{14}=95\) है। \(a_{23}\) क्या होगा?
In an arithmetic sequence, \(a_5=32\) and \(a_{14}=95\). What is \(a_{23}\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (154)
B (156)
C (158)
D (160)
Explanation opens after your attempt
Step 1
Concept
From (9d=63), (d=7), so \(a_{23}=95+9\cdot7=158\). It is easier to find a distant term from a nearby given term.
Step 2
Why this answer is correct
The correct answer is C. (158). From (9d=63), (d=7), so \(a_{23}=95+9\cdot7=158\). It is easier to find a distant term from a nearby given term.
Step 3
Exam Tip
(9d=63) से (d=7), इसलिए \(a_{23}=95+9\cdot7=158\)। निकट दिए गए पद से दूर का पद निकालना आसान है।
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श्रेणी \(1,7,17,31,49,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(1,7,17,31,49,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(2n^2-1\)
B \(n^2+3n-3\)
C \(2n^2+n-2\)
D \(3n^2-2n\)
Explanation opens after your attempt
Correct Answer
A. \(2n^2-1\)
Step 1
Concept
The given terms match \(2n^2-1\). Test options using the first term (1) and the second term (7).
Step 2
Why this answer is correct
The correct answer is A. \(2n^2-1\). The given terms match \(2n^2-1\). Test options using the first term (1) and the second term (7).
Step 3
Exam Tip
दिए गए पद \(2n^2-1\) से मिलते हैं। पहले पद (1) और दूसरे पद (7) से विकल्प जांचें।
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यदि \(a_n=6n-8\), तो \(a_{3n-2}\) क्या होगा?
If \(a_n=6n-8\), what is \(a_{3n-2}\)?
#sequences
#progressions
#nth-term
#algebra
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A (18n-8)
B (18n-20)
C (18n-12)
D (6n-20)
Explanation opens after your attempt
Correct Answer
B. (18n-20)
Step 1
Concept
Replacing (n) by (3n-2), (6(3n-2)-8=18n-20). Put the whole index in brackets while solving.
Step 2
Why this answer is correct
The correct answer is B. (18n-20). Replacing (n) by (3n-2), (6(3n-2)-8=18n-20). Put the whole index in brackets while solving.
Step 3
Exam Tip
(n) की जगह (3n-2) रखने पर (6(3n-2)-8=18n-20)। पूरे सूचकांक को ब्रैकेट में रखकर हल करें।
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श्रेणी \(19,31,43,55,\ldots\) में (151) कौन सा पद है?
In the sequence \(19,31,43,55,\ldots\), which term is (151)?
#sequences
#progressions
#nth-term
#arithmetic
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A (11)वां / (11)th
B (12)वां / (12)th
C (13)वां / (13)th
D (14)वां / (14)th
Explanation opens after your attempt
Correct Answer
B. (12)वां / (12)th
Step 1
Concept
From (19+(n-1)12=151), (n-1=11), so (n=12). Do not forget (n-1) while finding the term number.
Step 2
Why this answer is correct
The correct answer is B. (12)वां / (12)th. From (19+(n-1)12=151), (n-1=11), so (n=12). Do not forget (n-1) while finding the term number.
Step 3
Exam Tip
(19+(n-1)12=151) से (n-1=11), इसलिए (n=12)। पद संख्या निकालते समय (n-1) को न भूलें।
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यदि (a_n=\frac{n(n+5)}{3}), तो \(a_{12}\) का मान क्या होगा?
If (a_n=\frac{n(n+5)}{3}), what is the value of \(a_{12}\)?
#sequences
#progressions
#nth-term
#formula
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A (64)
B (66)
C (68)
D (72)
Explanation opens after your attempt
Step 1
Concept
(a_{12}=\frac{12(17)}{3}=68). Simplifying first makes fraction calculation easier.
Step 2
Why this answer is correct
The correct answer is C. (68). (a_{12}=\frac{12(17)}{3}=68). Simplifying first makes fraction calculation easier.
Step 3
Exam Tip
(a_{12}=\frac{12(17)}{3}=68)। भिन्न में पहले सरल करना गणना आसान बनाता है।
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श्रेणी \(8,21,40,65,96,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(8,21,40,65,96,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(2n^2+5n+1\)
B \(3n^2+4n+1\)
C \(n^2+10n-3\)
D \(3n^2+5n\)
Explanation opens after your attempt
Correct Answer
B. \(3n^2+4n+1\)
Step 1
Concept
The second differences are (6), and \(3n^2+4n+1\) gives all starting terms. In a quadratic sequence, test options on the first three terms.
Step 2
Why this answer is correct
The correct answer is B. \(3n^2+4n+1\). The second differences are (6), and \(3n^2+4n+1\) gives all starting terms. In a quadratic sequence, test options on the first three terms.
Step 3
Exam Tip
दूसरे अंतर (6) हैं और \(3n^2+4n+1\) सभी शुरुआती पद देता है। द्विघात श्रेणी में विकल्पों को पहले तीन पदों पर जांचें।
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यदि \(a_n=7\cdot2^{n-1}-3\), तो \(a_5\) का मान क्या होगा?
If \(a_n=7\cdot2^{n-1}-3\), what is the value of \(a_5\)?
#sequences
#progressions
#nth-term
#exponential
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A (105)
B (107)
C (109)
D (111)
Explanation opens after your attempt
Step 1
Concept
\(a_5=7\cdot2^4-3=109\). Keep the exponent (n-1) correctly.
Step 2
Why this answer is correct
The correct answer is C. (109). \(a_5=7\cdot2^4-3=109\). Keep the exponent (n-1) correctly.
Step 3
Exam Tip
\(a_5=7\cdot2^4-3=109\)। (n-1) वाली घात को सही रखें।
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श्रेणी \(3,-6,9,-12,15,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(3,-6,9,-12,15,\ldots\)?
#sequences
#progressions
#nth-term
#alternating
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A (3(-1)^n n)
B (3(-1)^{n+1}n)
C (3n)
D ((-1)^{n+1}n)
Explanation opens after your attempt
Correct Answer
B. (3(-1)^{n+1}n)
Step 1
Concept
For odd (n), terms are positive and for even (n), terms are negative, so (a_n=3(-1)^{n+1}n). In alternating signs, test first at (n=1).
Step 2
Why this answer is correct
The correct answer is B. (3(-1)^{n+1}n). For odd (n), terms are positive and for even (n), terms are negative, so (a_n=3(-1)^{n+1}n). In alternating signs, test first at (n=1).
Step 3
Exam Tip
विषम (n) पर पद धनात्मक और सम (n) पर ऋणात्मक है, इसलिए (a_n=3(-1)^{n+1}n)। वैकल्पिक चिन्ह में पहले (n=1) पर जांचें।
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यदि \(a_n=n^2+10\), तो कौन सा पद (131) है?
If \(a_n=n^2+10\), which term is (131)?
#sequences
#progressions
#nth-term
#term-number
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A (10)वां / (10)th
B (11)वां / (11)th
C (12)वां / (12)th
D कोई पूर्णांक पद नहीं / No integral term
Explanation opens after your attempt
Correct Answer
B. (11)वां / (11)th
Step 1
Concept
From \(n^2+10=131\), \(n^2=121\), so (n=11). A term number is taken as a positive integer.
Step 2
Why this answer is correct
The correct answer is B. (11)वां / (11)th. From \(n^2+10=131\), \(n^2=121\), so (n=11). A term number is taken as a positive integer.
Step 3
Exam Tip
\(n^2+10=131\) से \(n^2=121\), इसलिए (n=11)। पद संख्या धन पूर्णांक ही ली जाती है।
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श्रेणी \(24,12,6,3,\frac{3}{2},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(24,12,6,3,\frac{3}{2},\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A (24\left\(\frac{1}{2}\right\)^n)
B (12\left\(\frac{1}{2}\right\)^{n-1})
C (24\left\(\frac{1}{2}\right\)^{n-1})
D \(\frac{24}{n}\)
Explanation opens after your attempt
Correct Answer
C. (24\left\(\frac{1}{2}\right\)^{n-1})
Step 1
Concept
Each term is halved, so (a_n=24\left\(\frac{1}{2}\right\)^{n-1}). In a geometric sequence, the exponent starts with (n-1).
Step 2
Why this answer is correct
The correct answer is C. (24\left\(\frac{1}{2}\right\)^{n-1}). Each term is halved, so (a_n=24\left\(\frac{1}{2}\right\)^{n-1}). In a geometric sequence, the exponent starts with (n-1).
Step 3
Exam Tip
हर पद आधा हो रहा है इसलिए (a_n=24\left\(\frac{1}{2}\right\)^{n-1})। गुणोत्तर श्रेणी में घात (n-1) से शुरू होती है।
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किसी श्रेणी का \(a_n=4n^2-9n+7\) है। \(a_{10}-a_3\) का मान क्या है?
A sequence has \(a_n=4n^2-9n+7\). What is the value of \(a_{10}-a_3\)?
#sequences
#progressions
#nth-term
#quadratic
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A (295)
B (299)
C (301)
D (305)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=317\) and \(a_3=16\), so the difference is (301). Find both terms separately and subtract.
Step 2
Why this answer is correct
The correct answer is C. (301). \(a_{10}=317\) and \(a_3=16\), so the difference is (301). Find both terms separately and subtract.
Step 3
Exam Tip
\(a_{10}=317\) और \(a_3=16\), इसलिए अंतर (301) है। दोनों पद अलग-अलग निकालकर घटाएं।
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श्रेणी \(18,35,52,69,\ldots\) का (25)वां पद क्या होगा?
What is the (25)th term of the sequence \(18,35,52,69,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (426)
B (424)
C (432)
D (418)
Explanation opens after your attempt
Step 1
Concept
The first term is (18) and the difference is (17), so \(a_{25}=18+24\cdot17=426\). The (25)th term includes (24) differences.
Step 2
Why this answer is correct
The correct answer is A. (426). The first term is (18) and the difference is (17), so \(a_{25}=18+24\cdot17=426\). The (25)th term includes (24) differences.
Step 3
Exam Tip
पहला पद (18) और अंतर (17) है, इसलिए \(a_{25}=18+24\cdot17=426\)। (25)वें पद में (24) अंतर जुड़ते हैं।
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यदि \(a_n=3n^2+4n\), तो \(a_7-a_4\) का मान क्या है?
If \(a_n=3n^2+4n\), what is the value of \(a_7-a_4\)?
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#progressions
#nth-term
#quadratic
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A (105)
B (108)
C (111)
D (114)
Explanation opens after your attempt
Step 1
Concept
\(a_7=175\) and \(a_4=64\), so the difference is (111). Find both terms correctly before subtracting.
Step 2
Why this answer is correct
The correct answer is C. (111). \(a_7=175\) and \(a_4=64\), so the difference is (111). Find both terms correctly before subtracting.
Step 3
Exam Tip
\(a_7=175\) और \(a_4=64\), इसलिए अंतर (111) है। घटाने से पहले दोनों पद सही निकालें।
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श्रेणी \(6,24,54,96,150,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(6,24,54,96,150,\ldots\)?
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#progressions
#nth-term
#squares
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A \(6n^2\)
B \(3n^2+3n\)
C \(2n^2+4n\)
D \(6n^2+6\)
Explanation opens after your attempt
Correct Answer
A. \(6n^2\)
Step 1
Concept
The terms are \(6\cdot1^2,6\cdot2^2,6\cdot3^2,\ldots\), so \(a_n=6n^2\). Identify the coefficient of the square pattern.
Step 2
Why this answer is correct
The correct answer is A. \(6n^2\). The terms are \(6\cdot1^2,6\cdot2^2,6\cdot3^2,\ldots\), so \(a_n=6n^2\). Identify the coefficient of the square pattern.
Step 3
Exam Tip
पद \(6\cdot1^2,6\cdot2^2,6\cdot3^2,\ldots\) हैं इसलिए \(a_n=6n^2\)। वर्ग पैटर्न के गुणांक को पहचानें।
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यदि \(a_n=40-7n\), तो \(a_n=5\) कब होगा?
If \(a_n=40-7n\), when will \(a_n=5\)?
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#nth-term
#equation
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A (4)वां / (4)th
B (5)वां / (5)th
C (6)वां / (6)th
D (7)वां / (7)th
Explanation opens after your attempt
Correct Answer
B. (5)वां / (5)th
Step 1
Concept
From (40-7n=5), (7n=35), so (n=5). Form an equation to find the term number.
Step 2
Why this answer is correct
The correct answer is B. (5)वां / (5)th. From (40-7n=5), (7n=35), so (n=5). Form an equation to find the term number.
Step 3
Exam Tip
(40-7n=5) से (7n=35), इसलिए (n=5)। समीकरण बनाकर पद संख्या निकालें।
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श्रेणी \(12,28,50,78,112,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(12,28,50,78,112,\ldots\)?
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#nth-term
#quadratic
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A \(2n^2+8n+2\)
B \(3n^2+7n+2\)
C \(n^2+13n-2\)
D \(3n^2+6n+3\)
Explanation opens after your attempt
Correct Answer
B. \(3n^2+7n+2\)
Step 1
Concept
The second differences are (6), and \(3n^2+7n+2\) gives the starting terms. In a quadratic rule, half of the second difference is the coefficient of \(n^2\).
Step 2
Why this answer is correct
The correct answer is B. \(3n^2+7n+2\). The second differences are (6), and \(3n^2+7n+2\) gives the starting terms. In a quadratic rule, half of the second difference is the coefficient of \(n^2\).
Step 3
Exam Tip
दूसरे अंतर (6) हैं और \(3n^2+7n+2\) शुरुआती पद देता है। द्विघात नियम में दूसरे अंतर का आधा \(n^2\) का गुणांक होता है।
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यदि \(a_n=5n+14\), तो \(a_{4p+2}\) क्या होगा?
If \(a_n=5n+14\), what is \(a_{4p+2}\)?
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#algebra
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A (20p+24)
B (20p+14)
C (20p+10)
D (5p+24)
Explanation opens after your attempt
Correct Answer
A. (20p+24)
Step 1
Concept
Putting (n=4p+2), (5(4p+2)+14=20p+24). Substitute the whole expression given in the index.
Step 2
Why this answer is correct
The correct answer is A. (20p+24). Putting (n=4p+2), (5(4p+2)+14=20p+24). Substitute the whole expression given in the index.
Step 3
Exam Tip
(n=4p+2) रखने पर (5(4p+2)+14=20p+24)। सूचकांक में दिया पूरा व्यंजक प्रतिस्थापित करें।
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श्रेणी \(5,7,11,19,35,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(5,7,11,19,35,\ldots\)?
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#nth-term
#exponential
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A \(2^n+3\)
B \(2^{n+1}+1\)
C \(2^n+n\)
D (3n+2)
Explanation opens after your attempt
Correct Answer
A. \(2^n+3\)
Step 1
Concept
The terms are \(2+3,4+3,8+3,\ldots\), so \(a_n=2^n+3\). In exponential patterns, identify the constant addition.
Step 2
Why this answer is correct
The correct answer is A. \(2^n+3\). The terms are \(2+3,4+3,8+3,\ldots\), so \(a_n=2^n+3\). In exponential patterns, identify the constant addition.
Step 3
Exam Tip
पद \(2+3,4+3,8+3,\ldots\) हैं इसलिए \(a_n=2^n+3\)। घातीय पैटर्न में स्थिर जोड़ को पहचानें।
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यदि (a_n=n(n+4)), तो कौन सा पद (77) है?
If (a_n=n(n+4)), which term is (77)?
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A (6)वां / (6)th
B (7)वां / (7)th
C (8)वां / (8)th
D (9)वां / (9)th
Explanation opens after your attempt
Correct Answer
B. (7)वां / (7)th
Step 1
Concept
Putting (n=7), (7(7+4)=77). Directly testing the options can be a quick method.
Step 2
Why this answer is correct
The correct answer is B. (7)वां / (7)th. Putting (n=7), (7(7+4)=77). Directly testing the options can be a quick method.
Step 3
Exam Tip
(n=7) रखने पर (7(7+4)=77)। विकल्पों को सीधे जांचना तेज तरीका हो सकता है।
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किसी समान्तर श्रेणी का (n)वां पद \(a_n=12n-7\) है। सामान्य अंतर क्या है?
The (n)th term of an arithmetic sequence is \(a_n=12n-7\). What is the common difference?
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A (7)
B (12)
C (19)
D (5)
Explanation opens after your attempt
Step 1
Concept
In \(a_n=12n-7\), the coefficient of (n) is (12), so the common difference is (12). In a linear (n)th term, the coefficient of (n) gives the difference.
Step 2
Why this answer is correct
The correct answer is B. (12). In \(a_n=12n-7\), the coefficient of (n) is (12), so the common difference is (12). In a linear (n)th term, the coefficient of (n) gives the difference.
Step 3
Exam Tip
\(a_n=12n-7\) में (n) का गुणांक (12) है, इसलिए सामान्य अंतर (12) है। रैखिक (n)वें पद में (n) का गुणांक अंतर देता है।
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श्रेणी \(81,27,9,3,1,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(81,27,9,3,1,\ldots\)?
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A (81\left\(\frac{1}{3}\right\)^n)
B (27\left\(\frac{1}{3}\right\)^{n-1})
C (81\left\(\frac{1}{3}\right\)^{n-1})
D \(\frac{81}{n}\)
Explanation opens after your attempt
Correct Answer
C. (81\left\(\frac{1}{3}\right\)^{n-1})
Step 1
Concept
Each term is multiplied by \(\frac{1}{3}\), so (a_n=81\left\(\frac{1}{3}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
Step 2
Why this answer is correct
The correct answer is C. (81\left\(\frac{1}{3}\right\)^{n-1}). Each term is multiplied by \(\frac{1}{3}\), so (a_n=81\left\(\frac{1}{3}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
Step 3
Exam Tip
हर पद \(\frac{1}{3}\) गुना हो रहा है इसलिए (a_n=81\left\(\frac{1}{3}\right\)^{n-1})। पहले पद को सुरक्षित रखकर (n-1) घात लगाएं।
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