अनुक्रम \(4,8,12,16,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,8,12,16,\ldots\)?
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A \(a_n=4n\)
B \(a_n=n+4\)
C \(a_n=3n+1\)
D \(a_n=4n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n\)
Step 1
Concept
Each term is a multiple of (4), so \(a_n=4n\). In exams, check multiple-based sequences using (kn).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n\). Each term is a multiple of (4), so \(a_n=4n\). In exams, check multiple-based sequences using (kn).
Step 3
Exam Tip
हर पद (4) का गुणज है, इसलिए \(a_n=4n\) है। परीक्षा में गुणज वाले अनुक्रमों को (kn) से जाँचें।
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यदि \(a_n=6n+2\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=6n+2\), what is the value of \(a_3\)?
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(a_3=6\times3+2=20\). In exams, multiply first and then add the constant.
Step 2
Why this answer is correct
The correct answer is B. (20). \(a_3=6\times3+2=20\). In exams, multiply first and then add the constant.
Step 3
Exam Tip
\(a_3=6\times3+2=20\) है। परीक्षा में पहले गुणा करें और फिर स्थिर संख्या जोड़ें।
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अनुक्रम \(11,22,33,44,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(11,22,33,44,\ldots\)?
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A \(a_n=10n+1\)
B \(a_n=n+11\)
C \(a_n=11n\)
D \(a_n=22n\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=11n\)
Step 1
Concept
Each term is a multiple of (11), so \(a_n=11n\) is correct. In exams, identify equal multiples directly.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=11n\). Each term is a multiple of (11), so \(a_n=11n\) is correct. In exams, identify equal multiples directly.
Step 3
Exam Tip
हर पद (11) का गुणज है, इसलिए \(a_n=11n\) सही है। परीक्षा में समान गुणजों को सीधे पहचानें।
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यदि \(a_n=9n-4\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=9n-4\), what is the value of \(a_4\)?
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A (28)
B (30)
C (32)
D (34)
Explanation opens after your attempt
Step 1
Concept
\(a_4=9\times4-4=32\). In exams, subtract only after multiplying.
Step 2
Why this answer is correct
The correct answer is C. (32). \(a_4=9\times4-4=32\). In exams, subtract only after multiplying.
Step 3
Exam Tip
\(a_4=9\times4-4=32\) है। परीक्षा में गुणा के बाद घटाव करें।
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अनुक्रम \(3,8,13,18,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,8,13,18,\ldots\)?
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A \(a_n=5n-2\)
B \(a_n=3n+5\)
C \(a_n=5n+2\)
D \(a_n=8n-5\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n-2\)
Step 1
Concept
The first term is (3) and the difference is (5), so \(a_n=5n-2\). In exams, take the difference as the coefficient of (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n-2\). The first term is (3) and the difference is (5), so \(a_n=5n-2\). In exams, take the difference as the coefficient of (n).
Step 3
Exam Tip
पहला पद (3) और अंतर (5) है, इसलिए \(a_n=5n-2\) है। परीक्षा में अंतर को (n) का गुणांक मानें।
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यदि \(a_n=n^2+3\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=n^2+3\), what is the value of \(a_5\)?
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A (25)
B (26)
C (27)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(a_5=5^2+3=28\). In exams, find the square first and then add (3).
Step 2
Why this answer is correct
The correct answer is D. (28). \(a_5=5^2+3=28\). In exams, find the square first and then add (3).
Step 3
Exam Tip
\(a_5=5^2+3=28\) है। परीक्षा में पहले वर्ग निकालें और फिर (3) जोड़ें।
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अनुक्रम \(4,7,12,19,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(4,7,12,19,\ldots\)?
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A \(a_n=2n+2\)
B \(a_n=n^2+3\)
C \(a_n=n^2+2n\)
D \(a_n=3n+1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+3\)
Step 1
Concept
Using \(n^2+3\) gives (4,7,12,19). In exams, test options by putting (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+3\). Using \(n^2+3\) gives (4,7,12,19). In exams, test options by putting (n=1,2,3).
Step 3
Exam Tip
\(n^2+3\) रखने पर (4,7,12,19) मिलते हैं। परीक्षा में विकल्पों में (n=1,2,3) रखकर जाँचें।
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यदि \(a_n=14-3n\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=14-3n\), what is the value of \(a_3\)?
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_3=14-9=5\). In exams, subtract (3n) correctly in a decreasing formula.
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_3=14-9=5\). In exams, subtract (3n) correctly in a decreasing formula.
Step 3
Exam Tip
\(a_3=14-9=5\) है। परीक्षा में घटते सूत्र में (3n) को सही घटाएँ।
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अनुक्रम \(11,8,5,2,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(11,8,5,2,\ldots\)?
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A \(a_n=11-3n\)
B \(a_n=14-3n\)
C \(a_n=3n+8\)
D \(a_n=8-n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=14-3n\)
Step 1
Concept
At (n=1) it gives (11), and at (n=2) it gives (8), so \(a_n=14-3n\). In exams, treat a decreasing difference as negative.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=14-3n\). At (n=1) it gives (11), and at (n=2) it gives (8), so \(a_n=14-3n\). In exams, treat a decreasing difference as negative.
Step 3
Exam Tip
(n=1) पर (11) और (n=2) पर (8) मिलता है, इसलिए \(a_n=14-3n\) है। परीक्षा में घटते अंतर को ऋणात्मक समझें।
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यदि \(a_n=5^n\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=5^n\), what is the value of \(a_2\)?
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A (10)
B (15)
C (25)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(a_2=5^2=25\). In exams, identify the base and exponent separately.
Step 2
Why this answer is correct
The correct answer is C. (25). \(a_2=5^2=25\). In exams, identify the base and exponent separately.
Step 3
Exam Tip
\(a_2=5^2=25\) है। परीक्षा में आधार और घातांक को अलग पहचानें।
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अनुक्रम \(5,25,125,625,\ldots\) के लिए सही नियम कौन-सा है?
Which rule is correct for the sequence \(5,25,125,625,\ldots\)?
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A \(a_n=5n\)
B \(a_n=5^n\)
C \(a_n=n^5\)
D \(a_n=5^n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=5^n\)
Step 1
Concept
These terms are consecutive powers of (5). In exams, check \(5^n\) when you see (5,25,125).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=5^n\). These terms are consecutive powers of (5). In exams, check \(5^n\) when you see (5,25,125).
Step 3
Exam Tip
ये पद (5) की क्रमिक घातें हैं। परीक्षा में (5,25,125) देखकर \(5^n\) जाँचें।
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यदि \(a_n=3n^2\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=3n^2\), what is the value of \(a_4\)?
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A (36)
B (42)
C (48)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(a_4=3\times4^2=48\). In exams, square first and then multiply by (3).
Step 2
Why this answer is correct
The correct answer is C. (48). \(a_4=3\times4^2=48\). In exams, square first and then multiply by (3).
Step 3
Exam Tip
\(a_4=3\times4^2=48\) है। परीक्षा में वर्ग निकालकर (3) से गुणा करें।
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अनुक्रम \(3,12,27,48,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,12,27,48,\ldots\)?
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A \(a_n=3n^2\)
B \(a_n=3n\)
C \(a_n=n^3\)
D \(a_n=4n^2-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2\)
Step 1
Concept
These terms come from \(3n^2\). In exams, test the square-based rule on the first three terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2\). These terms come from \(3n^2\). In exams, test the square-based rule on the first three terms.
Step 3
Exam Tip
ये पद \(3n^2\) से मिलते हैं। परीक्षा में वर्ग आधारित नियम को पहले तीन पदों पर जाँचें।
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यदि \(a_n=\frac{3n}{2}\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=\frac{3n}{2}\), what is the value of \(a_4\)?
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_4=\frac{3\times4}{2}=6\). In exams, simplify the fraction before answering.
Step 2
Why this answer is correct
The correct answer is C. (6). \(a_4=\frac{3\times4}{2}=6\). In exams, simplify the fraction before answering.
Step 3
Exam Tip
\(a_4=\frac{3\times4}{2}=6\) है। परीक्षा में भिन्न को सरल करके उत्तर दें।
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अनुक्रम \(\frac{3}{2},3,\frac{9}{2},6,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{3}{2},3,\frac{9}{2},6,\ldots\)?
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A \(a_n=\frac{n}{3}\)
B \(a_n=\frac{3n}{2}\)
C \(a_n=2n\)
D \(a_n=3n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{3n}{2}\)
Step 1
Concept
Each term is the next multiple of \(\frac{3}{2}\). In exams, write fractional multiples as (kn).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{3n}{2}\). Each term is the next multiple of \(\frac{3}{2}\). In exams, write fractional multiples as (kn).
Step 3
Exam Tip
हर पद \(\frac{3}{2}\) का अगला गुणज है। परीक्षा में भिन्न गुणजों को (kn) के रूप में लिखें।
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यदि \(a_n=2n-3\) है, तो कौन-सा पद (15) के बराबर होगा?
If \(a_n=2n-3\), which term will be equal to (15)?
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A (n=7)
B (n=8)
C (n=9)
D (n=10)
Explanation opens after your attempt
Step 1
Concept
From (2n-3=15), we get (n=9). In exams, equate the formula to the given value when term number is asked.
Step 2
Why this answer is correct
The correct answer is C. (n=9). From (2n-3=15), we get (n=9). In exams, equate the formula to the given value when term number is asked.
Step 3
Exam Tip
(2n-3=15) से (n=9) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(-1,1,3,5,\ldots\) में (15) कौन-सा पद है?
In the sequence \(-1,1,3,5,\ldots\), which term is (15)?
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A सातवाँ पद / (7)th term
B आठवाँ पद / (8)th term
C नौवाँ पद / (9)th term
D दसवाँ पद / (10)th term
Explanation opens after your attempt
Correct Answer
C. नौवाँ पद / (9)th term
Step 1
Concept
Its rule is \(a_n=2n-3\), and (2n-3=15) gives (n=9). In exams, form the general term first to find the term number.
Step 2
Why this answer is correct
The correct answer is C. नौवाँ पद / (9)th term. Its rule is \(a_n=2n-3\), and (2n-3=15) gives (n=9). In exams, form the general term first to find the term number.
Step 3
Exam Tip
इसका नियम \(a_n=2n-3\) है और (2n-3=15) से (n=9) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।
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यदि \(a_n=n^3\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=n^3\), what is the value of \(a_3\)?
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A (9)
B (18)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3^3=27\). In exams, multiply the number three times when finding a cube.
Step 2
Why this answer is correct
The correct answer is C. (27). \(a_3=3^3=27\). In exams, multiply the number three times when finding a cube.
Step 3
Exam Tip
\(a_3=3^3=27\) है। परीक्षा में घन निकालते समय संख्या को तीन बार गुणा करें।
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अनुक्रम \(1,8,27,64,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,8,27,64,\ldots\)?
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A \(a_n=n^2\)
B \(a_n=n^3\)
C \(a_n=3n\)
D \(a_n=2^n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^3\)
Step 1
Concept
These are perfect cubes, so \(a_n=n^3\). In exams, recognize (1,8,27,64) as cube numbers.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^3\). These are perfect cubes, so \(a_n=n^3\). In exams, recognize (1,8,27,64) as cube numbers.
Step 3
Exam Tip
ये पूर्ण घन हैं, इसलिए \(a_n=n^3\) है। परीक्षा में (1,8,27,64) को घन संख्याओं के रूप में पहचानें।
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यदि \(a_n=n^3+1\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=n^3+1\), what is the value of \(a_2\)?
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_2=2^3+1=9\). In exams, find the cube first and then add (1).
Step 2
Why this answer is correct
The correct answer is C. (9). \(a_2=2^3+1=9\). In exams, find the cube first and then add (1).
Step 3
Exam Tip
\(a_2=2^3+1=9\) है। परीक्षा में पहले घन निकालें और फिर (1) जोड़ें।
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अनुक्रम \(2,9,28,65,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,9,28,65,\ldots\)?
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A \(a_n=n^2+1\)
B \(a_n=n^3+1\)
C \(a_n=2n+1\)
D \(a_n=3^n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^3+1\)
Step 1
Concept
The terms come from \(n^3+1\). In exams, check options using (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^3+1\). The terms come from \(n^3+1\). In exams, check options using (n=1,2,3).
Step 3
Exam Tip
ये पद \(n^3+1\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प जाँचें।
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यदि \(a_n=20-4n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=20-4n\), what is the value of \(a_4\)?
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_4=20-16=4\). In exams, calculate (4n) and subtract it.
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_4=20-16=4\). In exams, calculate (4n) and subtract it.
Step 3
Exam Tip
\(a_4=20-16=4\) है। परीक्षा में (4n) निकालकर उसे घटाएँ।
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अनुक्रम \(16,12,8,4,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(16,12,8,4,\ldots\)?
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A \(a_n=16-4n\)
B \(a_n=20-4n\)
C \(a_n=4n\)
D \(a_n=12-n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=20-4n\)
Step 1
Concept
At (n=1) it gives (16), and at (n=2) it gives (12), so \(a_n=20-4n\). In exams, check the rule with the first term in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=20-4n\). At (n=1) it gives (16), and at (n=2) it gives (12), so \(a_n=20-4n\). In exams, check the rule with the first term in a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (16) और (n=2) पर (12) मिलता है, इसलिए \(a_n=20-4n\) है। परीक्षा में घटते अनुक्रम में पहला पद मिलाकर नियम जाँचें।
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यदि \(a_n=7n+1\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=7n+1\), what is the value of \(a_5\)?
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A (34)
B (35)
C (36)
D (37)
Explanation opens after your attempt
Step 1
Concept
\(a_5=7\times5+1=36\). In exams, add the constant at the end.
Step 2
Why this answer is correct
The correct answer is C. (36). \(a_5=7\times5+1=36\). In exams, add the constant at the end.
Step 3
Exam Tip
\(a_5=7\times5+1=36\) है। परीक्षा में स्थिर संख्या को अंत में जोड़ें।
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अनुक्रम \(8,15,22,29,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(8,15,22,29,\ldots\)?
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A \(a_n=7n+1\)
B \(a_n=8n\)
C \(a_n=7n-1\)
D \(a_n=n+7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7n+1\)
Step 1
Concept
The first term is (8) and the difference is (7), so \(a_n=7n+1\). In exams, find the constant part from the first term.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=7n+1\). The first term is (8) and the difference is (7), so \(a_n=7n+1\). In exams, find the constant part from the first term.
Step 3
Exam Tip
पहला पद (8) और अंतर (7) है, इसलिए \(a_n=7n+1\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।
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यदि (a_n=\frac{n(n-1)}{2}) है, तो \(a_5\) का मान क्या होगा?
If (a_n=\frac{n(n-1)}{2}), what is the value of \(a_5\)?
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A (8)
B (10)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(a_5=\frac{5\times4}{2}=10\). In exams, multiply first and then divide by (2).
Step 2
Why this answer is correct
The correct answer is B. (10). \(a_5=\frac{5\times4}{2}=10\). In exams, multiply first and then divide by (2).
Step 3
Exam Tip
\(a_5=\frac{5\times4}{2}=10\) है। परीक्षा में पहले गुणन करें और फिर (2) से भाग दें।
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अनुक्रम \(0,1,3,6,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(0,1,3,6,\ldots\)?
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A (a_n=\frac{n(n+1)}{2})
B (a_n=\frac{n(n-1)}{2})
C \(a_n=n^2-1\)
D \(a_n=n-1\)
Explanation opens after your attempt
Correct Answer
B. (a_n=\frac{n(n-1)}{2})
Step 1
Concept
Putting (n=1,2,3,4) gives (0,1,3,6). In exams, test triangular-number-like options with small (n).
Step 2
Why this answer is correct
The correct answer is B. (a_n=\frac{n(n-1)}{2}). Putting (n=1,2,3,4) gives (0,1,3,6). In exams, test triangular-number-like options with small (n).
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (0,1,3,6) मिलते हैं। परीक्षा में त्रिभुज संख्या जैसे विकल्पों को छोटे (n) से जाँचें।
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यदि \(a_n=4n^2-1\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=4n^2-1\), what is the value of \(a_3\)?
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A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
\(a_3=4\times9-1=35\). In exams, square first and then multiply by (4).
Step 2
Why this answer is correct
The correct answer is C. (35). \(a_3=4\times9-1=35\). In exams, square first and then multiply by (4).
Step 3
Exam Tip
\(a_3=4\times9-1=35\) है। परीक्षा में वर्ग के बाद (4) से गुणा करें।
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अनुक्रम \(3,15,35,63,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,15,35,63,\ldots\)?
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A \(a_n=4n-1\)
B \(a_n=4n^2-1\)
C \(a_n=n^2+2\)
D \(a_n=3n^2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n^2-1\)
Step 1
Concept
\(4n^2-1\) gives (3,15,35,63). In exams, substitute (n=1,2,3) and match.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n^2-1\). \(4n^2-1\) gives (3,15,35,63). In exams, substitute (n=1,2,3) and match.
Step 3
Exam Tip
\(4n^2-1\) से (3,15,35,63) मिलते हैं। परीक्षा में (n=1,2,3) रखकर मिलान करें।
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यदि \(a_n=3n+7\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=3n+7\), what is the value of \(a_6\)?
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A (23)
B (25)
C (27)
D (29)
Explanation opens after your attempt
Step 1
Concept
\(a_6=3\times6+7=25\). In exams, put the given (n) directly into the formula.
Step 2
Why this answer is correct
The correct answer is B. (25). \(a_6=3\times6+7=25\). In exams, put the given (n) directly into the formula.
Step 3
Exam Tip
\(a_6=3\times6+7=25\) है। परीक्षा में दिए (n) को सीधे सूत्र में रखें।
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अनुक्रम \(10,13,16,19,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(10,13,16,19,\ldots\)?
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A \(a_n=10n\)
B \(a_n=3n+7\)
C \(a_n=3n-7\)
D \(a_n=n+9\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3n+7\)
Step 1
Concept
The difference is (3) and the first term is (10), so \(a_n=3n+7\). In exams, check the rule on the first two terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3n+7\). The difference is (3) and the first term is (10), so \(a_n=3n+7\). In exams, check the rule on the first two terms.
Step 3
Exam Tip
अंतर (3) है और पहला पद (10) है, इसलिए \(a_n=3n+7\) है। परीक्षा में पहले दो पदों पर नियम जाँचें।
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यदि \(a_n=2^{n+1}\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=2^{n+1}\), what is the value of \(a_3\)?
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A (8)
B (12)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_3=2^4=16\). In exams, find the exponent (n+1) first.
Step 2
Why this answer is correct
The correct answer is C. (16). \(a_3=2^4=16\). In exams, find the exponent (n+1) first.
Step 3
Exam Tip
\(a_3=2^4=16\) है। परीक्षा में पहले घातांक (n+1) निकालें।
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अनुक्रम \(4,8,16,32,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,8,16,32,\ldots\)?
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A \(a_n=2n+2\)
B \(a_n=4n\)
C \(a_n=2^{n+1}\)
D \(a_n=2^n-1\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=2^{n+1}\)
Step 1
Concept
Using \(2^{n+1}\) gives (4,8,16,32). In exams, match power options with the first term.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=2^{n+1}\). Using \(2^{n+1}\) gives (4,8,16,32). In exams, match power options with the first term.
Step 3
Exam Tip
\(2^{n+1}\) रखने पर (4,8,16,32) मिलते हैं। परीक्षा में घात वाले विकल्पों को पहले पद से मिलाएँ।
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यदि \(a_n=n^2+2n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=n^2+2n\), what is the value of \(a_4\)?
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A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
\(a_4=16+8=24\). In exams, add both the square and (2n).
Step 2
Why this answer is correct
The correct answer is C. (24). \(a_4=16+8=24\). In exams, add both the square and (2n).
Step 3
Exam Tip
\(a_4=16+8=24\) है। परीक्षा में वर्ग और (2n) दोनों जोड़ें।
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अनुक्रम \(3,8,15,24,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(3,8,15,24,\ldots\)?
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A \(a_n=n^2+2n\)
B \(a_n=3n\)
C \(a_n=n^2+1\)
D \(a_n=2n^2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+2n\)
Step 1
Concept
\(n^2+2n\) gives (3,8,15,24). In exams, test polynomial rules with small (n) values.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+2n\). \(n^2+2n\) gives (3,8,15,24). In exams, test polynomial rules with small (n) values.
Step 3
Exam Tip
\(n^2+2n\) से (3,8,15,24) मिलते हैं। परीक्षा में बहुपद नियमों को छोटे (n) मानों से जाँचें।
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यदि \(a_n=50-5n\) है, तो \(a_7\) का मान क्या होगा?
If \(a_n=50-5n\), what is the value of \(a_7\)?
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A (10)
B (15)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
\(a_7=50-35=15\). In exams, subtract (5n) correctly.
Step 2
Why this answer is correct
The correct answer is B. (15). \(a_7=50-35=15\). In exams, subtract (5n) correctly.
Step 3
Exam Tip
\(a_7=50-35=15\) है। परीक्षा में (5n) को सही घटाएँ।
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अनुक्रम \(45,40,35,30,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(45,40,35,30,\ldots\)?
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A \(a_n=45-5n\)
B \(a_n=50-5n\)
C \(a_n=5n+40\)
D \(a_n=40-n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=50-5n\)
Step 1
Concept
At (n=1), it gives (45), and at (n=2), it gives (40), so \(a_n=50-5n\). In exams, always check (n=1) when forming a decreasing rule.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=50-5n\). At (n=1), it gives (45), and at (n=2), it gives (40), so \(a_n=50-5n\). In exams, always check (n=1) when forming a decreasing rule.
Step 3
Exam Tip
(n=1) पर (45) और (n=2) पर (40) मिलता है, इसलिए \(a_n=50-5n\) है। परीक्षा में घटते समान अंतर का नियम बनाते समय (n=1) जरूर जाँचें।
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यदि \(a_n=6n-5\) है, तो कौन-सा पद (31) के बराबर होगा?
If \(a_n=6n-5\), which term will be equal to (31)?
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A (n=4)
B (n=5)
C (n=6)
D (n=7)
Explanation opens after your attempt
Step 1
Concept
From (6n-5=31), we get (n=6). In exams, equate the given term to the formula and solve.
Step 2
Why this answer is correct
The correct answer is C. (n=6). From (6n-5=31), we get (n=6). In exams, equate the given term to the formula and solve.
Step 3
Exam Tip
(6n-5=31) से (n=6) मिलता है। परीक्षा में दिए पद को सूत्र के बराबर रखकर हल करें।
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अनुक्रम \(1,7,13,19,\ldots\) में (31) कौन-सा पद है?
In the sequence \(1,7,13,19,\ldots\), which term is (31)?
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A चौथा पद / (4)th term
B पाँचवाँ पद / (5)th term
C छठा पद / (6)th term
D सातवाँ पद / (7)th term
Explanation opens after your attempt
Correct Answer
C. छठा पद / (6)th term
Step 1
Concept
Its rule is \(a_n=6n-5\), and (6n-5=31) gives (n=6). In exams, form the general term to find the term number.
Step 2
Why this answer is correct
The correct answer is C. छठा पद / (6)th term. Its rule is \(a_n=6n-5\), and (6n-5=31) gives (n=6). In exams, form the general term to find the term number.
Step 3
Exam Tip
इसका नियम \(a_n=6n-5\) है और (6n-5=31) से (n=6) है। परीक्षा में सामान्य पद बनाकर पद संख्या निकालें।
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यदि \(a_n=\frac{n+1}{2}\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=\frac{n+1}{2}\), what is the value of \(a_5\)?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_5=\frac{6}{2}=3\). In exams, simplify the numerator before dividing by the denominator.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_5=\frac{6}{2}=3\). In exams, simplify the numerator before dividing by the denominator.
Step 3
Exam Tip
\(a_5=\frac{6}{2}=3\) है। परीक्षा में पहले हर में जाने से पहले अंश को सरल करें।
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अनुक्रम \(1,\frac{3}{2},2,\frac{5}{2},\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,\frac{3}{2},2,\frac{5}{2},\ldots\)?
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A \(a_n=\frac{n}{2}\)
B \(a_n=\frac{n+1}{2}\)
C \(a_n=n+1\)
D \(a_n=2n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{n+1}{2}\)
Step 1
Concept
\(\frac{n+1}{2}\) gives \(1,\frac{3}{2},2,\frac{5}{2}\). In exams, match fractional terms using small (n) values.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{n+1}{2}\). \(\frac{n+1}{2}\) gives \(1,\frac{3}{2},2,\frac{5}{2}\). In exams, match fractional terms using small (n) values.
Step 3
Exam Tip
\(\frac{n+1}{2}\) से \(1,\frac{3}{2},2,\frac{5}{2}\) मिलते हैं। परीक्षा में भिन्न पदों को छोटे (n) मानों से मिलाएँ।
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यदि \(a_n=10n+5\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=10n+5\), what is the value of \(a_2\)?
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A (15)
B (20)
C (25)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(a_2=10\times2+5=25\). In exams, replace (n) with the term number.
Step 2
Why this answer is correct
The correct answer is C. (25). \(a_2=10\times2+5=25\). In exams, replace (n) with the term number.
Step 3
Exam Tip
\(a_2=10\times2+5=25\) है। परीक्षा में (n) की जगह पद संख्या रखें।
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अनुक्रम \(15,25,35,45,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(15,25,35,45,\ldots\)?
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A \(a_n=15n\)
B \(a_n=10n+5\)
C \(a_n=5n+10\)
D \(a_n=10n-5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=10n+5\)
Step 1
Concept
The first term is (15) and the difference is (10), so \(a_n=10n+5\). In exams, use the difference as the coefficient and find the constant from the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=10n+5\). The first term is (15) and the difference is (10), so \(a_n=10n+5\). In exams, use the difference as the coefficient and find the constant from the first term.
Step 3
Exam Tip
पहला पद (15) और अंतर (10) है, इसलिए \(a_n=10n+5\) है। परीक्षा में अंतर को गुणांक और पहले पद से स्थिर भाग निकालें।
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यदि \(a_n=2n^2+1\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=2n^2+1\), what is the value of \(a_3\)?
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A (17)
B (19)
C (21)
D (23)
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times9+1=19\). In exams, square first, multiply by (2), and add (1).
Step 2
Why this answer is correct
The correct answer is B. (19). \(a_3=2\times9+1=19\). In exams, square first, multiply by (2), and add (1).
Step 3
Exam Tip
\(a_3=2\times9+1=19\) है। परीक्षा में वर्ग के बाद (2) से गुणा करें और (1) जोड़ें।
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अनुक्रम \(3,9,19,33,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,9,19,33,\ldots\)?
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#explicit-rule
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A \(a_n=2n^2+1\)
B \(a_n=3n\)
C \(a_n=n^2+2\)
D \(a_n=2^n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2n^2+1\)
Step 1
Concept
Using \(2n^2+1\) gives (3,9,19,33). In exams, match the square-based rule with the first four terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2n^2+1\). Using \(2n^2+1\) gives (3,9,19,33). In exams, match the square-based rule with the first four terms.
Step 3
Exam Tip
\(2n^2+1\) रखने पर (3,9,19,33) मिलते हैं। परीक्षा में वर्ग वाले नियम को पहले चार पदों से मिलाएँ।
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यदि \(a_n=3^n-2\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=3^n-2\), what is the value of \(a_3\)?
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A (23)
B (24)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3^3-2=25\). In exams, find the power first and then subtract (2).
Step 2
Why this answer is correct
The correct answer is C. (25). \(a_3=3^3-2=25\). In exams, find the power first and then subtract (2).
Step 3
Exam Tip
\(a_3=3^3-2=25\) है। परीक्षा में पहले घात निकालें और फिर (2) घटाएँ।
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अनुक्रम \(1,7,25,79,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(1,7,25,79,\ldots\)?
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A \(a_n=3^n\)
B \(a_n=3^n-2\)
C \(a_n=2^n-1\)
D \(a_n=n^3-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3^n-2\)
Step 1
Concept
\(3^n-2\) gives (1,7,25,79). In exams, also check constant subtraction in power-based options.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3^n-2\). \(3^n-2\) gives (1,7,25,79). In exams, also check constant subtraction in power-based options.
Step 3
Exam Tip
\(3^n-2\) से (1,7,25,79) मिलते हैं। परीक्षा में घात वाले विकल्पों में स्थिर घटाव भी जाँचें।
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यदि \(a_n=n^2-2n\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=n^2-2n\), what is the value of \(a_6\)?
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(a_6=36-12=24\). In exams, subtract (2n) from the square.
Step 2
Why this answer is correct
The correct answer is D. (24). \(a_6=36-12=24\). In exams, subtract (2n) from the square.
Step 3
Exam Tip
\(a_6=36-12=24\) है। परीक्षा में वर्ग में से (2n) घटाएँ।
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अनुक्रम \(-1,0,3,8,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(-1,0,3,8,\ldots\)?
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A \(a_n=n^2-2n\)
B \(a_n=n^2-1\)
C \(a_n=2n-3\)
D \(a_n=n^2+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-2n\)
Step 1
Concept
\(n^2-2n\) gives (-1,0,3,8). In exams, keep testing options even when the first term is negative.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-2n\). \(n^2-2n\) gives (-1,0,3,8). In exams, keep testing options even when the first term is negative.
Step 3
Exam Tip
\(n^2-2n\) से (-1,0,3,8) मिलते हैं। परीक्षा में ऋणात्मक पहला पद आने पर भी विकल्पों को जाँचें।
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यदि \(a_n=18+n\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=18+n\), what is the value of \(a_5\)?
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A (21)
B (22)
C (23)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(a_5=18+5=23\). In exams, substitute directly in simple addition formulas.
Step 2
Why this answer is correct
The correct answer is C. (23). \(a_5=18+5=23\). In exams, substitute directly in simple addition formulas.
Step 3
Exam Tip
\(a_5=18+5=23\) है। परीक्षा में सरल जोड़ वाले सूत्रों में सीधे प्रतिस्थापन करें।
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