अनुक्रम \(13,26,39,52,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(13,26,39,52,\ldots\)?
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A \(a_n=13n\)
B \(a_n=n+13\)
C \(a_n=12n+1\)
D \(a_n=26n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=13n\)
Step 1
Concept
Each term is a multiple of (13), so \(a_n=13n\). In exams, check multiple-based sequences using (kn).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=13n\). Each term is a multiple of (13), so \(a_n=13n\). In exams, check multiple-based sequences using (kn).
Step 3
Exam Tip
हर पद (13) का गुणज है, इसलिए \(a_n=13n\) है। परीक्षा में गुणज वाले अनुक्रम को (kn) से जाँचें।
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यदि \(a_n=12n+1\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=12n+1\), what is the value of \(a_2\)?
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A (23)
B (24)
C (25)
D (26)
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Step 1
Concept
\(a_2=12\times2+1=25\). In exams, multiply first and then add (1).
Step 2
Why this answer is correct
The correct answer is C. (25). \(a_2=12\times2+1=25\). In exams, multiply first and then add (1).
Step 3
Exam Tip
\(a_2=12\times2+1=25\) है। परीक्षा में पहले गुणा करें और फिर (1) जोड़ें।
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अनुक्रम \(2,7,12,17,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(2,7,12,17,\ldots\)?
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A \(a_n=5n+2\)
B \(a_n=5n-3\)
C \(a_n=2n+5\)
D \(a_n=7n-5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=5n-3\)
Step 1
Concept
The first term is (2) and the difference is (5), so \(a_n=5n-3\). In exams, always check the first term by putting (n=1).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=5n-3\). The first term is (2) and the difference is (5), so \(a_n=5n-3\). In exams, always check the first term by putting (n=1).
Step 3
Exam Tip
पहला पद (2) और अंतर (5) है, इसलिए \(a_n=5n-3\) है। परीक्षा में (n=1) रखकर पहला पद जरूर जाँचें।
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यदि \(a_n=8n+6\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=8n+6\), what is the value of \(a_3\)?
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A (28)
B (30)
C (32)
D (34)
Explanation opens after your attempt
Step 1
Concept
\(a_3=8\times3+6=30\). In exams, put the term number directly into the formula.
Step 2
Why this answer is correct
The correct answer is B. (30). \(a_3=8\times3+6=30\). In exams, put the term number directly into the formula.
Step 3
Exam Tip
\(a_3=8\times3+6=30\) है। परीक्षा में पद संख्या को सीधे सूत्र में रखें।
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अनुक्रम \(14,20,26,32,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(14,20,26,32,\ldots\)?
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A \(a_n=6n+8\)
B \(a_n=14n\)
C \(a_n=6n-8\)
D \(a_n=8n+6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n+8\)
Step 1
Concept
The difference is (6) and the first term is (14), so \(a_n=6n+8\). In exams, take the difference as the coefficient of (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n+8\). The difference is (6) and the first term is (14), so \(a_n=6n+8\). In exams, take the difference as the coefficient of (n).
Step 3
Exam Tip
अंतर (6) है और पहला पद (14) है, इसलिए \(a_n=6n+8\) है। परीक्षा में अंतर को (n) का गुणांक मानें।
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यदि \(a_n=n^2+4\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=n^2+4\), what is the value of \(a_4\)?
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A (18)
B (19)
C (20)
D (21)
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Step 1
Concept
\(a_4=4^2+4=20\). In exams, find the square first and then add (4).
Step 2
Why this answer is correct
The correct answer is C. (20). \(a_4=4^2+4=20\). In exams, find the square first and then add (4).
Step 3
Exam Tip
\(a_4=4^2+4=20\) है। परीक्षा में पहले वर्ग निकालें और फिर (4) जोड़ें।
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अनुक्रम \(5,8,13,20,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(5,8,13,20,\ldots\)?
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A \(a_n=2n+3\)
B \(a_n=n^2+4\)
C \(a_n=n^2+3\)
D \(a_n=4n+1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+4\)
Step 1
Concept
Using \(n^2+4\) gives (5,8,13,20). In exams, match options using (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+4\). Using \(n^2+4\) gives (5,8,13,20). In exams, match options using (n=1,2,3).
Step 3
Exam Tip
\(n^2+4\) रखने पर (5,8,13,20) मिलते हैं। परीक्षा में विकल्पों को (n=1,2,3) से मिलाएँ।
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यदि \(a_n=30-2n\) है, तो \(a_7\) का मान क्या होगा?
If \(a_n=30-2n\), what is the value of \(a_7\)?
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A (12)
B (14)
C (16)
D (18)
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Step 1
Concept
\(a_7=30-14=16\). In exams, subtract (2n) correctly in a decreasing formula.
Step 2
Why this answer is correct
The correct answer is C. (16). \(a_7=30-14=16\). In exams, subtract (2n) correctly in a decreasing formula.
Step 3
Exam Tip
\(a_7=30-14=16\) है। परीक्षा में घटते सूत्र में (2n) को सही घटाएँ।
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अनुक्रम \(28,26,24,22,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(28,26,24,22,\ldots\)?
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A \(a_n=28-2n\)
B \(a_n=30-2n\)
C \(a_n=2n+26\)
D \(a_n=28+n\)
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Correct Answer
B. \(a_n=30-2n\)
Step 1
Concept
At (n=1) it gives (28), and at (n=2) it gives (26), so \(a_n=30-2n\). In exams, treat a decreasing difference as negative.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=30-2n\). At (n=1) it gives (28), and at (n=2) it gives (26), so \(a_n=30-2n\). In exams, treat a decreasing difference as negative.
Step 3
Exam Tip
(n=1) पर (28) और (n=2) पर (26) मिलता है, इसलिए \(a_n=30-2n\) है। परीक्षा में घटते अंतर को ऋणात्मक मानें।
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यदि \(a_n=4^n\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=4^n\), what is the value of \(a_2\)?
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A (8)
B (12)
C (16)
D (20)
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Step 1
Concept
\(a_2=4^2=16\). In exams, identify the base and exponent separately.
Step 2
Why this answer is correct
The correct answer is C. (16). \(a_2=4^2=16\). In exams, identify the base and exponent separately.
Step 3
Exam Tip
\(a_2=4^2=16\) है। परीक्षा में आधार और घातांक को अलग पहचानें।
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अनुक्रम \(4,16,64,256,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(4,16,64,256,\ldots\)?
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A \(a_n=4n\)
B \(a_n=n^4\)
C \(a_n=4^n\)
D \(a_n=4^n-1\)
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Correct Answer
C. \(a_n=4^n\)
Step 1
Concept
These terms are consecutive powers of (4). In exams, check power rules in rapidly growing sequences.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=4^n\). These terms are consecutive powers of (4). In exams, check power rules in rapidly growing sequences.
Step 3
Exam Tip
ये पद (4) की क्रमिक घातें हैं। परीक्षा में तेज बढ़ते अनुक्रमों में घात वाले नियम जाँचें।
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यदि \(a_n=5n^2+2\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=5n^2+2\), what is the value of \(a_2\)?
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A (20)
B (22)
C (24)
D (26)
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Step 1
Concept
\(a_2=5\times4+2=22\). In exams, square first and then multiply by (5).
Step 2
Why this answer is correct
The correct answer is B. (22). \(a_2=5\times4+2=22\). In exams, square first and then multiply by (5).
Step 3
Exam Tip
\(a_2=5\times4+2=22\) है। परीक्षा में वर्ग निकालकर (5) से गुणा करें।
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अनुक्रम \(7,22,47,82,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(7,22,47,82,\ldots\)?
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A \(a_n=5n^2+2\)
B \(a_n=7n\)
C \(a_n=5n+2\)
D \(a_n=2n^2+5\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n^2+2\)
Step 1
Concept
\(5n^2+2\) gives (7,22,47,82). In exams, test square-based rules with small (n) values.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n^2+2\). \(5n^2+2\) gives (7,22,47,82). In exams, test square-based rules with small (n) values.
Step 3
Exam Tip
\(5n^2+2\) से (7,22,47,82) मिलते हैं। परीक्षा में वर्ग आधारित नियमों को छोटे (n) मानों से जाँचें।
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यदि \(a_n=\frac{5n}{2}\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=\frac{5n}{2}\), what is the value of \(a_6\)?
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A (10)
B (12)
C (15)
D (18)
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Step 1
Concept
\(a_6=\frac{5\times6}{2}=15\). In exams, simplify the fraction before answering.
Step 2
Why this answer is correct
The correct answer is C. (15). \(a_6=\frac{5\times6}{2}=15\). In exams, simplify the fraction before answering.
Step 3
Exam Tip
\(a_6=\frac{5\times6}{2}=15\) है। परीक्षा में भिन्न को सरल करके उत्तर दें।
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अनुक्रम \(\frac{5}{2},5,\frac{15}{2},10,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{5}{2},5,\frac{15}{2},10,\ldots\)?
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A \(a_n=\frac{5n}{2}\)
B \(a_n=\frac{n}{5}\)
C \(a_n=5n\)
D \(a_n=2n+5\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{5n}{2}\)
Step 1
Concept
Each term is the next multiple of \(\frac{5}{2}\). In exams, write fractional multiples as (kn).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{5n}{2}\). Each term is the next multiple of \(\frac{5}{2}\). In exams, write fractional multiples as (kn).
Step 3
Exam Tip
हर पद \(\frac{5}{2}\) का अगला गुणज है। परीक्षा में भिन्न गुणजों को (kn) के रूप में लिखें।
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यदि \(a_n=4n-7\) है, तो कौन-सा पद (25) के बराबर होगा?
If \(a_n=4n-7\), which term will be equal to (25)?
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A (n=6)
B (n=7)
C (n=8)
D (n=9)
Explanation opens after your attempt
Step 1
Concept
From (4n-7=25), we get (n=8). In exams, when the term number is asked, equate the formula to the given value.
Step 2
Why this answer is correct
The correct answer is C. (n=8). From (4n-7=25), we get (n=8). In exams, when the term number is asked, equate the formula to the given value.
Step 3
Exam Tip
(4n-7=25) से (n=8) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(-3,1,5,9,\ldots\) में (25) कौन-सा पद है?
In the sequence \(-3,1,5,9,\ldots\), which term is (25)?
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A छठा पद / (6)th term
B सातवाँ पद / (7)th term
C आठवाँ पद / (8)th term
D नौवाँ पद / (9)th term
Explanation opens after your attempt
Correct Answer
C. आठवाँ पद / (8)th term
Step 1
Concept
Its rule is \(a_n=4n-7\), and (4n-7=25) gives (n=8). In exams, form the general term first to find the term number.
Step 2
Why this answer is correct
The correct answer is C. आठवाँ पद / (8)th term. Its rule is \(a_n=4n-7\), and (4n-7=25) gives (n=8). In exams, form the general term first to find the term number.
Step 3
Exam Tip
इसका नियम \(a_n=4n-7\) है और (4n-7=25) से (n=8) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।
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यदि \(a_n=n^3-1\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=n^3-1\), what is the value of \(a_3\)?
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A (24)
B (25)
C (26)
D (27)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3^3-1=26\). In exams, find the cube first and then subtract (1).
Step 2
Why this answer is correct
The correct answer is C. (26). \(a_3=3^3-1=26\). In exams, find the cube first and then subtract (1).
Step 3
Exam Tip
\(a_3=3^3-1=26\) है। परीक्षा में पहले घन निकालें और फिर (1) घटाएँ।
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अनुक्रम \(0,7,26,63,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(0,7,26,63,\ldots\)?
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A \(a_n=n^2-1\)
B \(a_n=n^3-1\)
C \(a_n=3n-3\)
D \(a_n=2^n-2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^3-1\)
Step 1
Concept
\(n^3-1\) gives (0,7,26,63). In exams, match cube-based options with the first four terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^3-1\). \(n^3-1\) gives (0,7,26,63). In exams, match cube-based options with the first four terms.
Step 3
Exam Tip
\(n^3-1\) से (0,7,26,63) मिलते हैं। परीक्षा में घन वाले विकल्पों को पहले चार पदों से मिलाएँ।
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यदि \(a_n=2n^3\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=2n^3\), what is the value of \(a_2\)?
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A (12)
B (14)
C (16)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(a_2=2\times2^3=16\). In exams, cube first and then multiply by (2).
Step 2
Why this answer is correct
The correct answer is C. (16). \(a_2=2\times2^3=16\). In exams, cube first and then multiply by (2).
Step 3
Exam Tip
\(a_2=2\times2^3=16\) है। परीक्षा में घन के बाद (2) से गुणा करें।
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अनुक्रम \(2,16,54,128,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,16,54,128,\ldots\)?
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A \(a_n=2n^3\)
B \(a_n=2n^2\)
C \(a_n=n^3+1\)
D \(a_n=4n^2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2n^3\)
Step 1
Concept
These terms come from \(2n^3\). In exams, check the rule by putting (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2n^3\). These terms come from \(2n^3\). In exams, check the rule by putting (n=1,2,3).
Step 3
Exam Tip
ये पद \(2n^3\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर नियम जाँचें।
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यदि \(a_n=40-3n\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=40-3n\), what is the value of \(a_5\)?
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A (21)
B (23)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
\(a_5=40-15=25\). In exams, subtract (3n) correctly.
Step 2
Why this answer is correct
The correct answer is C. (25). \(a_5=40-15=25\). In exams, subtract (3n) correctly.
Step 3
Exam Tip
\(a_5=40-15=25\) है। परीक्षा में (3n) को सही घटाएँ।
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अनुक्रम \(37,34,31,28,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(37,34,31,28,\ldots\)?
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A \(a_n=37-3n\)
B \(a_n=40-3n\)
C \(a_n=3n+34\)
D \(a_n=40+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=40-3n\)
Step 1
Concept
At (n=1) it gives (37), and at (n=2) it gives (34), so \(a_n=40-3n\). In exams, check a decreasing rule with the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=40-3n\). At (n=1) it gives (37), and at (n=2) it gives (34), so \(a_n=40-3n\). In exams, check a decreasing rule with the first term.
Step 3
Exam Tip
(n=1) पर (37) और (n=2) पर (34) मिलता है, इसलिए \(a_n=40-3n\) है। परीक्षा में घटते नियम को पहले पद से जाँचें।
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यदि \(a_n=9n+2\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=9n+2\), what is the value of \(a_4\)?
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A (36)
B (37)
C (38)
D (39)
Explanation opens after your attempt
Step 1
Concept
\(a_4=9\times4+2=38\). In exams, add the constant at the end.
Step 2
Why this answer is correct
The correct answer is C. (38). \(a_4=9\times4+2=38\). In exams, add the constant at the end.
Step 3
Exam Tip
\(a_4=9\times4+2=38\) है। परीक्षा में स्थिर संख्या को अंत में जोड़ें।
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अनुक्रम \(11,20,29,38,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(11,20,29,38,\ldots\)?
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A \(a_n=11n\)
B \(a_n=9n+2\)
C \(a_n=9n-2\)
D \(a_n=2n+9\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=9n+2\)
Step 1
Concept
The first term is (11) and the difference is (9), so \(a_n=9n+2\). In exams, check the rule on the first two terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=9n+2\). The first term is (11) and the difference is (9), so \(a_n=9n+2\). In exams, check the rule on the first two terms.
Step 3
Exam Tip
पहला पद (11) और अंतर (9) है, इसलिए \(a_n=9n+2\) है। परीक्षा में पहले दो पदों पर नियम जाँचें।
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यदि (a_n=\frac{n(n+3)}{2}) है, तो \(a_3\) का मान क्या होगा?
If (a_n=\frac{n(n+3)}{2}), what is the value of \(a_3\)?
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_3=\frac{3\times6}{2}=9\). In exams, find (n+3) first and then simplify.
Step 2
Why this answer is correct
The correct answer is C. (9). \(a_3=\frac{3\times6}{2}=9\). In exams, find (n+3) first and then simplify.
Step 3
Exam Tip
\(a_3=\frac{3\times6}{2}=9\) है। परीक्षा में पहले (n+3) निकालें और फिर सरल करें।
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अनुक्रम \(2,5,9,14,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,5,9,14,\ldots\)?
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A \(a_n=n+1\)
B (a_n=\frac{n(n+3)}{2})
C \(a_n=n^2+1\)
D \(a_n=2n+1\)
Explanation opens after your attempt
Correct Answer
B. (a_n=\frac{n(n+3)}{2})
Step 1
Concept
(\frac{n(n+3)}{2}) gives (2,5,9,14). In exams, test fractional formulas with small (n) values.
Step 2
Why this answer is correct
The correct answer is B. (a_n=\frac{n(n+3)}{2}). (\frac{n(n+3)}{2}) gives (2,5,9,14). In exams, test fractional formulas with small (n) values.
Step 3
Exam Tip
(\frac{n(n+3)}{2}) से (2,5,9,14) मिलते हैं। परीक्षा में भिन्न सूत्रों को छोटे (n) मानों से जाँचें।
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यदि \(a_n=6n^2-2\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=6n^2-2\), what is the value of \(a_2\)?
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A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
\(a_2=6\times4-2=22\). In exams, square first, multiply by (6), and subtract (2).
Step 2
Why this answer is correct
The correct answer is B. (22). \(a_2=6\times4-2=22\). In exams, square first, multiply by (6), and subtract (2).
Step 3
Exam Tip
\(a_2=6\times4-2=22\) है। परीक्षा में वर्ग के बाद (6) से गुणा करें और (2) घटाएँ।
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अनुक्रम \(4,22,52,94,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,22,52,94,\ldots\)?
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A \(a_n=6n^2-2\)
B \(a_n=4n\)
C \(a_n=6n-2\)
D \(a_n=2n^2+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n^2-2\)
Step 1
Concept
Using \(6n^2-2\) gives (4,22,52,94). In exams, match the square rule with the first three terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n^2-2\). Using \(6n^2-2\) gives (4,22,52,94). In exams, match the square rule with the first three terms.
Step 3
Exam Tip
\(6n^2-2\) रखने पर (4,22,52,94) मिलते हैं। परीक्षा में वर्ग वाले नियम को पहले तीन पदों से मिलाएँ।
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यदि \(a_n=4n+9\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=4n+9\), what is the value of \(a_6\)?
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A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
\(a_6=4\times6+9=33\). In exams, put the given (n) directly into the formula.
Step 2
Why this answer is correct
The correct answer is B. (33). \(a_6=4\times6+9=33\). In exams, put the given (n) directly into the formula.
Step 3
Exam Tip
\(a_6=4\times6+9=33\) है। परीक्षा में दिए (n) को सीधे सूत्र में रखें।
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अनुक्रम \(13,17,21,25,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(13,17,21,25,\ldots\)?
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A \(a_n=13n\)
B \(a_n=4n+9\)
C \(a_n=4n-9\)
D \(a_n=n+12\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n+9\)
Step 1
Concept
The difference is (4) and the first term is (13), so \(a_n=4n+9\). In exams, match both the difference and the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n+9\). The difference is (4) and the first term is (13), so \(a_n=4n+9\). In exams, match both the difference and the first term.
Step 3
Exam Tip
अंतर (4) है और पहला पद (13) है, इसलिए \(a_n=4n+9\) है। परीक्षा में अंतर और पहला पद दोनों मिलाएँ।
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यदि \(a_n=3^{n+1}\) है, तो \(a_2\) का मान क्या होगा?
If \(a_n=3^{n+1}\), what is the value of \(a_2\)?
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A (18)
B (24)
C (27)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(a_2=3^3=27\). In exams, find the exponent (n+1) first.
Step 2
Why this answer is correct
The correct answer is C. (27). \(a_2=3^3=27\). In exams, find the exponent (n+1) first.
Step 3
Exam Tip
\(a_2=3^3=27\) है। परीक्षा में पहले घातांक (n+1) निकालें।
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अनुक्रम \(9,27,81,243,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(9,27,81,243,\ldots\)?
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A \(a_n=9n\)
B \(a_n=3^n\)
C \(a_n=3^{n+1}\)
D \(a_n=n^3\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=3^{n+1}\)
Step 1
Concept
\(3^{n+1}\) gives (9,27,81,243). In exams, use the first term to identify the exponent shift.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=3^{n+1}\). \(3^{n+1}\) gives (9,27,81,243). In exams, use the first term to identify the exponent shift.
Step 3
Exam Tip
\(3^{n+1}\) से (9,27,81,243) मिलते हैं। परीक्षा में पहले पद देखकर घातांक का बदलाव पहचानें।
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यदि \(a_n=n^2+3n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=n^2+3n\), what is the value of \(a_4\)?
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A (26)
B (28)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_4=16+12=28\). In exams, add both the square and (3n).
Step 2
Why this answer is correct
The correct answer is B. (28). \(a_4=16+12=28\). In exams, add both the square and (3n).
Step 3
Exam Tip
\(a_4=16+12=28\) है। परीक्षा में वर्ग और (3n) दोनों जोड़ें।
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अनुक्रम \(4,10,18,28,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(4,10,18,28,\ldots\)?
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A \(a_n=n^2+3n\)
B \(a_n=4n\)
C \(a_n=n^2+2n\)
D \(a_n=3n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+3n\)
Step 1
Concept
Using \(n^2+3n\) gives (4,10,18,28). In exams, test the polynomial rule with the first four terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+3n\). Using \(n^2+3n\) gives (4,10,18,28). In exams, test the polynomial rule with the first four terms.
Step 3
Exam Tip
\(n^2+3n\) रखने पर (4,10,18,28) मिलते हैं। परीक्षा में बहुपद नियम को पहले चार पदों से जाँचें।
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यदि \(a_n=60-6n\) है, तो \(a_8\) का मान क्या होगा?
If \(a_n=60-6n\), what is the value of \(a_8\)?
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(a_8=60-48=12\). In exams, subtract (6n) correctly.
Step 2
Why this answer is correct
The correct answer is B. (12). \(a_8=60-48=12\). In exams, subtract (6n) correctly.
Step 3
Exam Tip
\(a_8=60-48=12\) है। परीक्षा में (6n) को सही घटाएँ।
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अनुक्रम \(54,48,42,36,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(54,48,42,36,\ldots\)?
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A \(a_n=54-6n\)
B \(a_n=60-6n\)
C \(a_n=6n+48\)
D \(a_n=60+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=60-6n\)
Step 1
Concept
At (n=1) it gives (54), and at (n=2) it gives (48), so \(a_n=60-6n\). In exams, check a decreasing sequence rule using (n=1).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=60-6n\). At (n=1) it gives (54), and at (n=2) it gives (48), so \(a_n=60-6n\). In exams, check a decreasing sequence rule using (n=1).
Step 3
Exam Tip
(n=1) पर (54) और (n=2) पर (48) मिलता है, इसलिए \(a_n=60-6n\) है। परीक्षा में घटते अनुक्रम में (n=1) से नियम जाँचें।
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यदि \(a_n=7n-8\) है, तो कौन-सा पद (41) के बराबर होगा?
If \(a_n=7n-8\), which term will be equal to (41)?
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A (n=5)
B (n=6)
C (n=7)
D (n=8)
Explanation opens after your attempt
Step 1
Concept
From (7n-8=41), we get (n=7). In exams, equate the given value to the formula and solve.
Step 2
Why this answer is correct
The correct answer is C. (n=7). From (7n-8=41), we get (n=7). In exams, equate the given value to the formula and solve.
Step 3
Exam Tip
(7n-8=41) से (n=7) मिलता है। परीक्षा में दिए मान को सूत्र के बराबर रखकर हल करें।
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अनुक्रम \(-1,6,13,20,\ldots\) में (41) कौन-सा पद है?
In the sequence \(-1,6,13,20,\ldots\), which term is (41)?
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A पाँचवाँ पद / (5)th term
B छठा पद / (6)th term
C सातवाँ पद / (7)th term
D आठवाँ पद / (8)th term
Explanation opens after your attempt
Correct Answer
C. सातवाँ पद / (7)th term
Step 1
Concept
Its rule is \(a_n=7n-8\), and (7n-8=41) gives (n=7). In exams, find the term number from the general term.
Step 2
Why this answer is correct
The correct answer is C. सातवाँ पद / (7)th term. Its rule is \(a_n=7n-8\), and (7n-8=41) gives (n=7). In exams, find the term number from the general term.
Step 3
Exam Tip
इसका नियम \(a_n=7n-8\) है और (7n-8=41) से (n=7) है। परीक्षा में सामान्य पद से पद संख्या निकालें।
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यदि \(a_n=\frac{2n+1}{3}\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=\frac{2n+1}{3}\), what is the value of \(a_4\)?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_4=\frac{9}{3}=3\). In exams, simplify the numerator first and then divide.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_4=\frac{9}{3}=3\). In exams, simplify the numerator first and then divide.
Step 3
Exam Tip
\(a_4=\frac{9}{3}=3\) है। परीक्षा में पहले अंश को सरल करें और फिर भाग दें।
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अनुक्रम \(1,\frac{5}{3},\frac{7}{3},3,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,\frac{5}{3},\frac{7}{3},3,\ldots\)?
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A \(a_n=\frac{n+2}{3}\)
B \(a_n=\frac{2n+1}{3}\)
C \(a_n=2n+1\)
D \(a_n=\frac{3n}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{2n+1}{3}\)
Step 1
Concept
\(\frac{2n+1}{3}\) gives \(1,\frac{5}{3},\frac{7}{3},3\). In exams, match fractional rules with small (n) values.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{2n+1}{3}\). \(\frac{2n+1}{3}\) gives \(1,\frac{5}{3},\frac{7}{3},3\). In exams, match fractional rules with small (n) values.
Step 3
Exam Tip
\(\frac{2n+1}{3}\) से \(1,\frac{5}{3},\frac{7}{3},3\) मिलते हैं। परीक्षा में भिन्न नियमों को छोटे (n) मानों से मिलाएँ।
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यदि \(a_n=11n+4\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=11n+4\), what is the value of \(a_3\)?
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A (35)
B (37)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
\(a_3=11\times3+4=37\). In exams, multiply first and then add the constant.
Step 2
Why this answer is correct
The correct answer is B. (37). \(a_3=11\times3+4=37\). In exams, multiply first and then add the constant.
Step 3
Exam Tip
\(a_3=11\times3+4=37\) है। परीक्षा में गुणा के बाद स्थिर संख्या जोड़ें।
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अनुक्रम \(15,26,37,48,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(15,26,37,48,\ldots\)?
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A \(a_n=15n\)
B \(a_n=11n+4\)
C \(a_n=11n-4\)
D \(a_n=4n+11\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=11n+4\)
Step 1
Concept
The first term is (15) and the difference is (11), so \(a_n=11n+4\). In exams, use the difference as coefficient and find the constant from the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=11n+4\). The first term is (15) and the difference is (11), so \(a_n=11n+4\). In exams, use the difference as coefficient and find the constant from the first term.
Step 3
Exam Tip
पहला पद (15) और अंतर (11) है, इसलिए \(a_n=11n+4\) है। परीक्षा में अंतर को गुणांक और पहले पद से स्थिर भाग निकालें।
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यदि \(a_n=3n^2+2n\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=3n^2+2n\), what is the value of \(a_3\)?
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#progressions
#explicit-rule
#class-9
#easy
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A (29)
B (31)
C (33)
D (35)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3\times9+6=33\). In exams, add both the square part and the linear part.
Step 2
Why this answer is correct
The correct answer is C. (33). \(a_3=3\times9+6=33\). In exams, add both the square part and the linear part.
Step 3
Exam Tip
\(a_3=3\times9+6=33\) है। परीक्षा में वर्ग वाला भाग और रैखिक भाग दोनों जोड़ें।
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अनुक्रम \(5,16,33,56,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,16,33,56,\ldots\)?
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#progressions
#explicit-rule
#class-9
#easy
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A \(a_n=3n^2+2n\)
B \(a_n=5n\)
C \(a_n=2n^2+3n\)
D \(a_n=3n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+2n\)
Step 1
Concept
\(3n^2+2n\) gives (5,16,33,56). In exams, substitute (n=1,2,3) and match.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+2n\). \(3n^2+2n\) gives (5,16,33,56). In exams, substitute (n=1,2,3) and match.
Step 3
Exam Tip
\(3n^2+2n\) से (5,16,33,56) मिलते हैं। परीक्षा में (n=1,2,3) रखकर मिलान करें।
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यदि \(a_n=2^n+3\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=2^n+3\), what is the value of \(a_4\)?
#sequences
#progressions
#explicit-rule
#class-9
#easy
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A (17)
B (18)
C (19)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(a_4=2^4+3=19\). In exams, find the power first and then add (3).
Step 2
Why this answer is correct
The correct answer is C. (19). \(a_4=2^4+3=19\). In exams, find the power first and then add (3).
Step 3
Exam Tip
\(a_4=2^4+3=19\) है। परीक्षा में पहले घात निकालें और फिर (3) जोड़ें।
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अनुक्रम \(5,7,11,19,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(5,7,11,19,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
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A \(a_n=2n+3\)
B \(a_n=2^n+3\)
C \(a_n=n^2+4\)
D \(a_n=3^n+2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=2^n+3\)
Step 1
Concept
\(2^n+3\) gives (5,7,11,19). In exams, also check constant addition in power-based options.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=2^n+3\). \(2^n+3\) gives (5,7,11,19). In exams, also check constant addition in power-based options.
Step 3
Exam Tip
\(2^n+3\) से (5,7,11,19) मिलते हैं। परीक्षा में घात वाले विकल्पों में स्थिर जोड़ भी जाँचें।
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यदि \(a_n=n^2-3n\) है, तो \(a_7\) का मान क्या होगा?
If \(a_n=n^2-3n\), what is the value of \(a_7\)?
#sequences
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#explicit-rule
#class-9
#easy
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A (24)
B (26)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(a_7=49-21=28\). In exams, subtract (3n) from the square.
Step 2
Why this answer is correct
The correct answer is C. (28). \(a_7=49-21=28\). In exams, subtract (3n) from the square.
Step 3
Exam Tip
\(a_7=49-21=28\) है। परीक्षा में वर्ग में से (3n) घटाएँ।
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अनुक्रम \(-2,-2,0,4,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(-2,-2,0,4,\ldots\)?
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#explicit-rule
#class-9
#easy
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A \(a_n=n^2-3n\)
B \(a_n=n^2-2\)
C \(a_n=2n-4\)
D \(a_n=n^2+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-3n\)
Step 1
Concept
\(n^2-3n\) gives (-2,-2,0,4). In exams, do not reject a rule just because terms are zero or negative.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-3n\). \(n^2-3n\) gives (-2,-2,0,4). In exams, do not reject a rule just because terms are zero or negative.
Step 3
Exam Tip
\(n^2-3n\) से (-2,-2,0,4) मिलते हैं। परीक्षा में शून्य या ऋणात्मक पद देखकर नियम को न छोड़ें।
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यदि \(a_n=25+n\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=25+n\), what is the value of \(a_6\)?
#sequences
#progressions
#explicit-rule
#class-9
#easy
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A (29)
B (30)
C (31)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_6=25+6=31\). In exams, substitute directly in simple addition formulas.
Step 2
Why this answer is correct
The correct answer is C. (31). \(a_6=25+6=31\). In exams, substitute directly in simple addition formulas.
Step 3
Exam Tip
\(a_6=25+6=31\) है। परीक्षा में सरल जोड़ वाले सूत्रों में सीधे प्रतिस्थापन करें।
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