अनुक्रम \(3,6,9,12,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,6,9,12,\ldots\)?
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A \(a_n=n+3\)
B \(a_n=2n\)
C \(a_n=3n\)
D \(a_n=3n+1\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=3n\)
Step 1
Concept
Each term is a multiple of (3), so \(a_n=3n\). In exams, match the first few terms with (n).
Step 2
Why this answer is correct
The correct answer is C. \(a_n=3n\). Each term is a multiple of (3), so \(a_n=3n\). In exams, match the first few terms with (n).
Step 3
Exam Tip
हर पद (3) का गुणज है, इसलिए \(a_n=3n\) है। परीक्षा में पहले कुछ पदों को (n) से मिलाकर देखें।
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अनुक्रम \(5,10,15,20,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(5,10,15,20,\ldots\)?
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A \(a_n=5n\)
B \(a_n=n+5\)
C \(a_n=4n\)
D \(a_n=5n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n\)
Step 1
Concept
This is the sequence of multiples of (5). In exams, quickly check \(a_n=dn\) for multiple-based sequences.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n\). This is the sequence of multiples of (5). In exams, quickly check \(a_n=dn\) for multiple-based sequences.
Step 3
Exam Tip
यह (5) के पहाड़े का अनुक्रम है। परीक्षा में गुणज वाले अनुक्रमों में \(a_n=dn\) तुरंत जाँचें।
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अनुक्रम \(2,4,6,8,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,4,6,8,\ldots\)?
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A \(a_n=n\)
B \(a_n=2n\)
C \(a_n=2n+1\)
D \(a_n=n+2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=2n\)
Step 1
Concept
This is the sequence of even numbers, so \(a_n=2n\). In exams, remember (2n) for even numbers.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=2n\). This is the sequence of even numbers, so \(a_n=2n\). In exams, remember (2n) for even numbers.
Step 3
Exam Tip
यह सम संख्याओं का अनुक्रम है, इसलिए \(a_n=2n\) है। परीक्षा में सम संख्याओं के लिए (2n) याद रखें।
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अनुक्रम \(1,3,5,7,\ldots\) का स्पष्ट नियम कौन-सा है?
Which explicit rule represents the sequence \(1,3,5,7,\ldots\)?
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A \(a_n=2n\)
B \(a_n=n+1\)
C \(a_n=2n-1\)
D \(a_n=3n-2\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=2n-1\)
Step 1
Concept
This is the sequence of odd numbers, so \(a_n=2n-1\). In exams, check the rule by putting (n=1).
Step 2
Why this answer is correct
The correct answer is C. \(a_n=2n-1\). This is the sequence of odd numbers, so \(a_n=2n-1\). In exams, check the rule by putting (n=1).
Step 3
Exam Tip
यह विषम संख्याओं का अनुक्रम है, इसलिए \(a_n=2n-1\) है। परीक्षा में पहले पद के लिए (n=1) रखकर नियम जाँचें।
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यदि \(a_n=n^2\) है, तो अनुक्रम के पहले तीन पद क्या होंगे?
If \(a_n=n^2\), what are the first three terms of the sequence?
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A (1,2,3)
B (1,4,9)
C (2,4,6)
D (3,6,9)
Explanation opens after your attempt
Correct Answer
B. (1,4,9)
Step 1
Concept
Putting (n=1,2,3) gives (1,4,9). In exams, use small values of (n) for first terms.
Step 2
Why this answer is correct
The correct answer is B. (1,4,9). Putting (n=1,2,3) gives (1,4,9). In exams, use small values of (n) for first terms.
Step 3
Exam Tip
(n=1,2,3) रखने पर (1,4,9) मिलते हैं। परीक्षा में पहले पदों के लिए (n) के छोटे मान रखें।
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अनुक्रम \(4,7,10,13,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,7,10,13,\ldots\)?
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A \(a_n=3n+1\)
B \(a_n=4n\)
C \(a_n=3n-1\)
D \(a_n=n+3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n+1\)
Step 1
Concept
The first term is (4) and the difference is (3), so \(a_n=3n+1\). In exams, use (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n+1\). The first term is (4) and the difference is (3), so \(a_n=3n+1\). In exams, use (a_n=a+(n-1)d).
Step 3
Exam Tip
पहला पद (4) और अंतर (3) है, इसलिए \(a_n=3n+1\) है। परीक्षा में (a_n=a+(n-1)d) का प्रयोग करें।
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यदि \(a_n=4n-2\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=4n-2\), what is the value of \(a_6\)?
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A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
\(a_6=4\times6-2=22\). In exams, multiply first and subtract afterward.
Step 2
Why this answer is correct
The correct answer is B. (22). \(a_6=4\times6-2=22\). In exams, multiply first and subtract afterward.
Step 3
Exam Tip
\(a_6=4\times6-2=22\) है। परीक्षा में गुणा पहले और घटाव बाद में करें।
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अनुक्रम \(10,20,30,40,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(10,20,30,40,\ldots\)?
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A \(a_n=n+10\)
B \(a_n=5n\)
C \(a_n=10n\)
D \(a_n=10n-1\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=10n\)
Step 1
Concept
Each term is a multiple of (10), so \(a_n=10n\). In exams, write the rule by observing the common difference of multiples.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=10n\). Each term is a multiple of (10), so \(a_n=10n\). In exams, write the rule by observing the common difference of multiples.
Step 3
Exam Tip
हर पद (10) का गुणज है, इसलिए \(a_n=10n\) है। परीक्षा में गुणजों का अंतर देखकर नियम लिखें।
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यदि \(a_n=7n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=7n\), what is the value of \(a_4\)?
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A (21)
B (24)
C (27)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(a_4=7\times4=28\). In exams, replace (n) with the term number.
Step 2
Why this answer is correct
The correct answer is D. (28). \(a_4=7\times4=28\). In exams, replace (n) with the term number.
Step 3
Exam Tip
\(a_4=7\times4=28\) है। परीक्षा में (n) की जगह पद संख्या रखें।
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अनुक्रम \(6,11,16,21,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(6,11,16,21,\ldots\)?
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A \(a_n=5n+1\)
B \(a_n=6n\)
C \(a_n=5n-1\)
D \(a_n=n+5\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n+1\)
Step 1
Concept
The first term is (6) and the difference is (5), so \(a_n=5n+1\). In exams, check the formula on the first two terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n+1\). The first term is (6) and the difference is (5), so \(a_n=5n+1\). In exams, check the formula on the first two terms.
Step 3
Exam Tip
पहला पद (6) और अंतर (5) है, इसलिए \(a_n=5n+1\) है। परीक्षा में सूत्र को पहले दो पदों पर जाँचें।
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यदि \(a_n=n+9\) है, तो अनुक्रम का पहला पद क्या है?
If \(a_n=n+9\), what is the first term of the sequence?
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
For the first term, putting (n=1) gives \(a_1=10\). In exams, always put (n=1) for the first term.
Step 2
Why this answer is correct
The correct answer is B. (10). For the first term, putting (n=1) gives \(a_1=10\). In exams, always put (n=1) for the first term.
Step 3
Exam Tip
पहले पद के लिए (n=1) रखने पर \(a_1=10\) मिलता है। परीक्षा में पहले पद के लिए हमेशा (n=1) रखें।
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अनुक्रम \(9,18,27,36,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(9,18,27,36,\ldots\)?
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A \(a_n=8n\)
B \(a_n=n+9\)
C \(a_n=9n\)
D \(a_n=9n+1\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=9n\)
Step 1
Concept
This is the sequence of multiples of (9). In exams, write (kn) for the (n)th multiple.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=9n\). This is the sequence of multiples of (9). In exams, write (kn) for the (n)th multiple.
Step 3
Exam Tip
यह (9) के गुणजों का अनुक्रम है। परीक्षा में (n)वें गुणज के लिए (kn) लिखें।
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यदि \(a_n=3n+2\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=3n+2\), what is the value of \(a_3\)?
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A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3\times3+2=11\). In exams, put the term number directly into the formula.
Step 2
Why this answer is correct
The correct answer is D. (11). \(a_3=3\times3+2=11\). In exams, put the term number directly into the formula.
Step 3
Exam Tip
\(a_3=3\times3+2=11\) है। परीक्षा में पद संख्या को सीधे सूत्र में रखें।
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अनुक्रम \(7,14,21,28,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(7,14,21,28,\ldots\)?
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A \(a_n=n+7\)
B \(a_n=7n\)
C \(a_n=6n+1\)
D \(a_n=7n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=7n\)
Step 1
Concept
Each term is obtained by multiplying by (7), so \(a_n=7n\). In exams, identify table-based sequences quickly.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=7n\). Each term is obtained by multiplying by (7), so \(a_n=7n\). In exams, identify table-based sequences quickly.
Step 3
Exam Tip
हर पद (7) से गुणा करके मिलता है, इसलिए \(a_n=7n\) है। परीक्षा में पहाड़े वाले अनुक्रम जल्दी पहचानें।
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यदि \(a_n=2n+5\) है, तो \(a_1\) और \(a_2\) क्या होंगे?
If \(a_n=2n+5\), what are \(a_1\) and \(a_2\)?
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A (7,9)
B (6,8)
C (5,7)
D (8,10)
Explanation opens after your attempt
Step 1
Concept
Putting (n=1) and (n=2) gives (7) and (9). In exams, find the first two terms to check the rule.
Step 2
Why this answer is correct
The correct answer is A. (7,9). Putting (n=1) and (n=2) gives (7) and (9). In exams, find the first two terms to check the rule.
Step 3
Exam Tip
(n=1) और (n=2) रखने पर (7) और (9) मिलते हैं। परीक्षा में पहले दो पद निकालकर नियम की जाँच करें।
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अनुक्रम \(12,15,18,21,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(12,15,18,21,\ldots\)?
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A \(a_n=3n+12\)
B \(a_n=12n\)
C \(a_n=3n+9\)
D \(a_n=4n+8\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=3n+9\)
Step 1
Concept
The first term is (12) and the difference is (3), so \(a_n=3n+9\). In exams, simplify (a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is C. \(a_n=3n+9\). The first term is (12) and the difference is (3), so \(a_n=3n+9\). In exams, simplify (a+(n-1)d).
Step 3
Exam Tip
पहला पद (12) और अंतर (3) है, इसलिए \(a_n=3n+9\) है। परीक्षा में (a+(n-1)d) को सरल करें।
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यदि \(a_n=6n-1\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=6n-1\), what is the value of \(a_5\)?
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A (25)
B (27)
C (29)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(a_5=6\times5-1=29\). In exams, do not forget the final subtraction.
Step 2
Why this answer is correct
The correct answer is C. (29). \(a_5=6\times5-1=29\). In exams, do not forget the final subtraction.
Step 3
Exam Tip
\(a_5=6\times5-1=29\) है। परीक्षा में अंतिम घटाव को भूलें नहीं।
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अनुक्रम \(1,4,9,16,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,4,9,16,\ldots\)?
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A \(a_n=n+1\)
B \(a_n=2n\)
C \(a_n=n^2\)
D \(a_n=3n\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=n^2\)
Step 1
Concept
These are perfect squares, so \(a_n=n^2\). In exams, recognize (1,4,9,16) as square numbers.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=n^2\). These are perfect squares, so \(a_n=n^2\). In exams, recognize (1,4,9,16) as square numbers.
Step 3
Exam Tip
ये पूर्ण वर्ग हैं, इसलिए \(a_n=n^2\) है। परीक्षा में (1,4,9,16) को वर्ग संख्याओं के रूप में पहचानें।
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यदि \(a_n=n^2+1\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=n^2+1\), what is the value of \(a_4\)?
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A (15)
B (16)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(a_4=4^2+1=17\). In exams, find the square and then add (1).
Step 2
Why this answer is correct
The correct answer is C. (17). \(a_4=4^2+1=17\). In exams, find the square and then add (1).
Step 3
Exam Tip
\(a_4=4^2+1=17\) है। परीक्षा में वर्ग निकालकर (1) जोड़ें।
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अनुक्रम \(2,5,10,17,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,5,10,17,\ldots\)?
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A \(a_n=n^2+1\)
B \(a_n=2n+1\)
C \(a_n=n^2\)
D \(a_n=3n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+1\)
Step 1
Concept
The terms are obtained from \(n^2+1\). In exams, check options by putting (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+1\). The terms are obtained from \(n^2+1\). In exams, check options by putting (n=1,2,3).
Step 3
Exam Tip
ये पद \(n^2+1\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प जाँचें।
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अनुक्रम \(9,8,7,6,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(9,8,7,6,\ldots\)?
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A \(a_n=10-n\)
B \(a_n=9+n\)
C \(a_n=n-10\)
D \(a_n=9n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=10-n\)
Step 1
Concept
\(At (n=1), it gives (9), and at (n=2), it gives (8). In exams, for a decreasing difference of (1), think (a_n=\)constant-n).
Step 2
Why this answer is correct
\(The correct answer is A. (a_n=10-n). At (n=1), it gives (9), and at (n=2), it gives (8). In exams, for a decreasing difference of (1), think (a_n=\)constant-n).
Step 3
Exam Tip
(n=1) पर (9) और (n=2) पर (8) मिलता है। \(परीक्षा में घटते हुए (1) के अंतर पर (a_n=\)स्थिर-n) सोचें।
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यदि \(a_n=15-2n\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=15-2n\), what is the value of \(a_5\)?
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_5=15-10=5\). In exams, calculate (2n) first.
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_5=15-10=5\). In exams, calculate (2n) first.
Step 3
Exam Tip
\(a_5=15-10=5\) है। परीक्षा में पहले (2n) का मान निकालें।
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अनुक्रम \(13,11,9,7,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(13,11,9,7,\ldots\)?
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A \(a_n=2n+11\)
B \(a_n=15-2n\)
C \(a_n=13-2n\)
D \(a_n=11+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=15-2n\)
Step 1
Concept
The first term is (13) and the difference is (-2), so \(a_n=15-2n\). In exams, treat a decreasing difference as negative.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=15-2n\). The first term is (13) and the difference is (-2), so \(a_n=15-2n\). In exams, treat a decreasing difference as negative.
Step 3
Exam Tip
पहला पद (13) है और अंतर (-2) है, इसलिए \(a_n=15-2n\) है। परीक्षा में घटते अंतर को ऋणात्मक मानें।
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यदि \(a_n=2^n\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=2^n\), what is the value of \(a_3\)?
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_3=2^3=8\). In exams, replace the exponent by the term number in power formulas.
Step 2
Why this answer is correct
The correct answer is C. (8). \(a_3=2^3=8\). In exams, replace the exponent by the term number in power formulas.
Step 3
Exam Tip
\(a_3=2^3=8\) है। परीक्षा में घात वाले सूत्र में घातांक को पद संख्या से बदलें।
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अनुक्रम \(2,4,8,16,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,4,8,16,\ldots\)?
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A \(a_n=2n\)
B \(a_n=n^2\)
C \(a_n=2^n\)
D \(a_n=2^n+1\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=2^n\)
Step 1
Concept
Each term is a power of (2), so \(a_n=2^n\). In exams, recognize geometric-type growth using powers.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=2^n\). Each term is a power of (2), so \(a_n=2^n\). In exams, recognize geometric-type growth using powers.
Step 3
Exam Tip
प्रत्येक पद (2) की घात है, इसलिए \(a_n=2^n\) है। परीक्षा में गुणोत्तर जैसी वृद्धि को घात से पहचानें।
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यदि \(a_n=3^n\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=3^n\), what is the value of \(a_2\)?
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A (6)
B (8)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(a_2=3^2=9\). In exams, identify the base and exponent separately.
Step 2
Why this answer is correct
The correct answer is C. (9). \(a_2=3^2=9\). In exams, identify the base and exponent separately.
Step 3
Exam Tip
\(a_2=3^2=9\) है। परीक्षा में आधार और घातांक को अलग पहचानें।
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अनुक्रम \(3,9,27,81,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(3,9,27,81,\ldots\)?
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A \(a_n=3n\)
B \(a_n=3^n\)
C \(a_n=n^3\)
D \(a_n=3^n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3^n\)
Step 1
Concept
These terms are consecutive powers of (3). In exams, check \(3^n\) when you see (3,9,27).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3^n\). These terms are consecutive powers of (3). In exams, check \(3^n\) when you see (3,9,27).
Step 3
Exam Tip
ये पद (3) की क्रमिक घातें हैं। परीक्षा में (3,9,27) देखकर \(3^n\) जाँचें।
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यदि \(a_n=n^2-n\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=n^2-n\), what is the value of \(a_5\)?
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A (15)
B (18)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
\(a_5=25-5=20\). In exams, find the square first and then subtract (n).
Step 2
Why this answer is correct
The correct answer is C. (20). \(a_5=25-5=20\). In exams, find the square first and then subtract (n).
Step 3
Exam Tip
\(a_5=25-5=20\) है। परीक्षा में पहले वर्ग निकालें और फिर (n) घटाएँ।
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अनुक्रम \(0,2,6,12,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(0,2,6,12,\ldots\)?
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A \(a_n=n^2-n\)
B \(a_n=n^2+1\)
C \(a_n=2n\)
D \(a_n=n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-n\)
Step 1
Concept
Using \(n^2-n\) gives (0,2,6,12). In exams, substitute (n=1,2,3) in the options to match.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-n\). Using \(n^2-n\) gives (0,2,6,12). In exams, substitute (n=1,2,3) in the options to match.
Step 3
Exam Tip
\(n^2-n\) रखने पर (0,2,6,12) मिलते हैं। परीक्षा में विकल्पों में (n=1,2,3) रखकर मिलान करें।
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यदि \(a_n=4n+3\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=4n+3\), what is the value of \(a_2\)?
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A (9)
B (11)
C (13)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(a_2=4\times2+3=11\). In exams, put (2) in place of (n) and simplify.
Step 2
Why this answer is correct
The correct answer is B. (11). \(a_2=4\times2+3=11\). In exams, put (2) in place of (n) and simplify.
Step 3
Exam Tip
\(a_2=4\times2+3=11\) है। परीक्षा में (n) की जगह (2) रखकर सरल करें।
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अनुक्रम \(7,11,15,19,\ldots\) के लिए सही नियम कौन-सा है?
Which rule is correct for the sequence \(7,11,15,19,\ldots\)?
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A \(a_n=4n+3\)
B \(a_n=7n\)
C \(a_n=4n-3\)
D \(a_n=n+6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n+3\)
Step 1
Concept
The first term is (7) and the difference is (4), so \(a_n=4n+3\). In exams, take the common difference as the coefficient of (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n+3\). The first term is (7) and the difference is (4), so \(a_n=4n+3\). In exams, take the common difference as the coefficient of (n).
Step 3
Exam Tip
पहला पद (7) और अंतर (4) है, इसलिए \(a_n=4n+3\) है। परीक्षा में अंतर को (n) का गुणांक मानें।
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यदि \(a_n=8n-3\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=8n-3\), what is the value of \(a_4\)?
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A (27)
B (29)
C (31)
D (33)
Explanation opens after your attempt
Step 1
Concept
\(a_4=8\times4-3=29\). In exams, subtract (3) only after multiplying.
Step 2
Why this answer is correct
The correct answer is B. (29). \(a_4=8\times4-3=29\). In exams, subtract (3) only after multiplying.
Step 3
Exam Tip
\(a_4=8\times4-3=29\) है। परीक्षा में गुणा के बाद ही (3) घटाएँ।
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अनुक्रम \(5,13,21,29,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,13,21,29,\ldots\)?
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A \(a_n=5n\)
B \(a_n=8n-3\)
C \(a_n=8n+3\)
D \(a_n=13n-8\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=8n-3\)
Step 1
Concept
The difference is (8), and at (n=1) the value must be (5), so \(a_n=8n-3\). In exams, find the constant using the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=8n-3\). The difference is (8), and at (n=1) the value must be (5), so \(a_n=8n-3\). In exams, find the constant using the first term.
Step 3
Exam Tip
अंतर (8) है और (n=1) पर (5) चाहिए, इसलिए \(a_n=8n-3\) है। परीक्षा में पहले पद से स्थिर संख्या निकालें।
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यदि \(a_n=\frac{n}{2}\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=\frac{n}{2}\), what is the value of \(a_6\)?
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_6=\frac{6}{2}=3\). In exams, substitute (n) first in fractional formulas.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_6=\frac{6}{2}=3\). In exams, substitute (n) first in fractional formulas.
Step 3
Exam Tip
\(a_6=\frac{6}{2}=3\) है। परीक्षा में भिन्न वाले सूत्र में पहले (n) रखें।
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अनुक्रम \(\frac{1}{2},1,\frac{3}{2},2,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?
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A \(a_n=n\)
B \(a_n=\frac{n}{2}\)
C \(a_n=2n\)
D \(a_n=n+1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{n}{2}\)
Step 1
Concept
Each term is half of (n). In exams, match fractional sequences using small values of (n).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{n}{2}\). Each term is half of (n). In exams, match fractional sequences using small values of (n).
Step 3
Exam Tip
हर पद (n) का आधा है। परीक्षा में भिन्न अनुक्रम को छोटे (n) मानों से मिलाएँ।
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अनुक्रम \(2,8,18,32,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,8,18,32,\ldots\)?
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A \(a_n=2n\)
B \(a_n=n^2+1\)
C \(a_n=2n^2\)
D \(a_n=4n\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=2n^2\)
Step 1
Concept
These terms come from \(2n^2\). In exams, test the square-based option on the first three terms.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=2n^2\). These terms come from \(2n^2\). In exams, test the square-based option on the first three terms.
Step 3
Exam Tip
ये पद \(2n^2\) से मिलते हैं। परीक्षा में वर्ग वाले विकल्प को पहले तीन पदों पर जाँचें।
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यदि \(a_n=3n-2\) है, तो कौन-सा पद (13) के बराबर होगा?
If \(a_n=3n-2\), which term will be equal to (13)?
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A (n=3)
B (n=4)
C (n=5)
D (n=6)
Explanation opens after your attempt
Step 1
Concept
From (3n-2=13), we get (n=5). In exams, when term number is asked, equate the formula to the given value.
Step 2
Why this answer is correct
The correct answer is C. (n=5). From (3n-2=13), we get (n=5). In exams, when term number is asked, equate the formula to the given value.
Step 3
Exam Tip
(3n-2=13) से (n=5) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(1,4,7,10,\ldots\) में (16) कौन-सा पद है?
In the sequence \(1,4,7,10,\ldots\), which term is (16)?
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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 \(a_n=3n-2\), and (3n-2=16) gives (n=6). In exams, form the general term first 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 \(a_n=3n-2\), and (3n-2=16) gives (n=6). In exams, form the general term first to find the term number.
Step 3
Exam Tip
इसका नियम \(a_n=3n-2\) है और (3n-2=16) से (n=6) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।
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यदि \(a_n=n+4\) है, तो \(a_7\) का मान क्या होगा?
If \(a_n=n+4\), what is the value of \(a_7\)?
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(a_7=7+4=11\). In exams, substitute directly in simple linear formulas.
Step 2
Why this answer is correct
The correct answer is C. (11). \(a_7=7+4=11\). In exams, substitute directly in simple linear formulas.
Step 3
Exam Tip
\(a_7=7+4=11\) है। परीक्षा में सरल रैखिक सूत्रों में सीधे प्रतिस्थापन करें।
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अनुक्रम \(5,6,7,8,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,6,7,8,\ldots\)?
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A \(a_n=n+4\)
B \(a_n=5n\)
C \(a_n=n+5\)
D \(a_n=4n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n+4\)
Step 1
Concept
When (n=1), the value should be (5), so \(a_n=n+4\). In exams, relate (n) to the first term in consecutive-number sequences.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n+4\). When (n=1), the value should be (5), so \(a_n=n+4\). In exams, relate (n) to the first term in consecutive-number sequences.
Step 3
Exam Tip
जब (n=1), तब मान (5) चाहिए, इसलिए \(a_n=n+4\) है। परीक्षा में लगातार संख्याओं में पहले पद से (n) का संबंध देखें।
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यदि \(a_n=12n\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=12n\), what is the value of \(a_3\)?
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A (24)
B (30)
C (36)
D (48)
Explanation opens after your attempt
Step 1
Concept
\(a_3=12\times3=36\). In exams, use the multiplication table.
Step 2
Why this answer is correct
The correct answer is C. (36). \(a_3=12\times3=36\). In exams, use the multiplication table.
Step 3
Exam Tip
\(a_3=12\times3=36\) है। परीक्षा में गुणा तालिका का उपयोग करें।
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अनुक्रम \(12,24,36,48,\ldots\) का स्पष्ट नियम क्या है?
What is the explicit rule of the sequence \(12,24,36,48,\ldots\)?
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A \(a_n=10n+2\)
B \(a_n=12n\)
C \(a_n=n+12\)
D \(a_n=24n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=12n\)
Step 1
Concept
Every term is a multiple of (12). In exams, write equal multiples as \(a_n=kn\).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=12n\). Every term is a multiple of (12). In exams, write equal multiples as \(a_n=kn\).
Step 3
Exam Tip
हर पद (12) का गुणज है। परीक्षा में समान गुणजों को \(a_n=kn\) से लिखें।
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यदि \(a_n=5n+4\) है, तो \(a_1\) का मान क्या होगा?
If \(a_n=5n+4\), what is the value of \(a_1\)?
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A (5)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_1=5\times1+4=9\). In exams, put (n=1) for the first term.
Step 2
Why this answer is correct
The correct answer is C. (9). \(a_1=5\times1+4=9\). In exams, put (n=1) for the first term.
Step 3
Exam Tip
\(a_1=5\times1+4=9\) है। परीक्षा में पहले पद के लिए (n=1) रखें।
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अनुक्रम \(9,14,19,24,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(9,14,19,24,\ldots\)?
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#explicit-rule
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A \(a_n=5n+4\)
B \(a_n=9n\)
C \(a_n=5n-4\)
D \(a_n=n+8\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n+4\)
Step 1
Concept
The first term is (9) and the difference is (5), so \(a_n=5n+4\). In exams, find the constant part from the first term.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n+4\). The first term is (9) and the difference is (5), so \(a_n=5n+4\). In exams, find the constant part from the first term.
Step 3
Exam Tip
पहला पद (9) और अंतर (5) है, इसलिए \(a_n=5n+4\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।
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यदि (a_n=\frac{n(n+1)}{2}) है, तो \(a_4\) का मान क्या होगा?
If (a_n=\frac{n(n+1)}{2}), what is the value of \(a_4\)?
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A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(a_4=\frac{4\times5}{2}=10\). In exams, first find (n(n+1)) and then divide by (2).
Step 2
Why this answer is correct
The correct answer is B. (10). \(a_4=\frac{4\times5}{2}=10\). In exams, first find (n(n+1)) and then divide by (2).
Step 3
Exam Tip
\(a_4=\frac{4\times5}{2}=10\) है। परीक्षा में पहले (n(n+1)) निकालें और फिर (2) से भाग दें।
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अनुक्रम \(1,3,6,10,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,3,6,10,\ldots\)?
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A \(a_n=n^2\)
B \(a_n=2n-1\)
C (a_n=\frac{n(n+1)}{2})
D \(a_n=n+2\)
Explanation opens after your attempt
Correct Answer
C. (a_n=\frac{n(n+1)}{2})
Step 1
Concept
This is the sequence of triangular numbers. In exams, check (\frac{n(n+1)}{2}) when you see (1,3,6,10).
Step 2
Why this answer is correct
The correct answer is C. (a_n=\frac{n(n+1)}{2}). This is the sequence of triangular numbers. In exams, check (\frac{n(n+1)}{2}) when you see (1,3,6,10).
Step 3
Exam Tip
यह त्रिभुज संख्याओं का अनुक्रम है। परीक्षा में (1,3,6,10) देखकर (\frac{n(n+1)}{2}) जाँचें।
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यदि \(a_n=100-5n\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=100-5n\), what is the value of \(a_6\)?
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A (60)
B (65)
C (70)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(a_6=100-30=70\). In exams, subtract (5n) correctly.
Step 2
Why this answer is correct
The correct answer is C. (70). \(a_6=100-30=70\). In exams, subtract (5n) correctly.
Step 3
Exam Tip
\(a_6=100-30=70\) है। परीक्षा में (5n) को सही घटाएँ।
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अनुक्रम \(4,16,36,64,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,16,36,64,\ldots\)?
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A \(a_n=2n^2\)
B \(a_n=4n^2\)
C \(a_n=n^2+4\)
D \(a_n=4n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n^2\)
Step 1
Concept
These terms are (4) times square numbers, so \(a_n=4n^2\). In exams, substitute (n=1,2,3) to match.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n^2\). These terms are (4) times square numbers, so \(a_n=4n^2\). In exams, substitute (n=1,2,3) to match.
Step 3
Exam Tip
ये पद (4) गुना वर्ग संख्याएँ हैं, इसलिए \(a_n=4n^2\) है। परीक्षा में (n=1,2,3) रखकर मिलान करें।
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यदि \(a_n=2^n-1\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=2^n-1\), what is the value of \(a_4\)?
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A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(a_4=2^4-1=15\). In exams, find the power first and then subtract (1).
Step 2
Why this answer is correct
The correct answer is C. (15). \(a_4=2^4-1=15\). In exams, find the power first and then subtract (1).
Step 3
Exam Tip
\(a_4=2^4-1=15\) है। परीक्षा में पहले घात निकालें और फिर (1) घटाएँ।
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अनुक्रम \(20,17,14,11,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(20,17,14,11,\ldots\)?
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A \(a_n=23-3n\)
B \(a_n=20-3n\)
C \(a_n=3n+17\)
D \(a_n=20+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=23-3n\)
Step 1
Concept
The first term is (20) and the difference is (-3), so \(a_n=23-3n\). In exams, treat the common difference as negative in decreasing sequences.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=23-3n\). The first term is (20) and the difference is (-3), so \(a_n=23-3n\). In exams, treat the common difference as negative in decreasing sequences.
Step 3
Exam Tip
पहला पद (20) और अंतर (-3) है, इसलिए \(a_n=23-3n\) है। परीक्षा में घटते अनुक्रम में अंतर को ऋणात्मक मानें।
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