अनुक्रम \(4,9,14,19,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,9,14,19,\ldots\)?
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A \(a_n=5n+1\)
B \(a_n=5n-1\)
C \(a_n=4n+5\)
D \(a_n=n+4\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=5n-1\)
Step 1
Concept
The first term is (4) and the difference is (5), so \(a_n=5n-1\). In exams, always check the first term by putting (n=1).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=5n-1\). The first term is (4) and the difference is (5), so \(a_n=5n-1\). In exams, always check the first term by putting (n=1).
Step 3
Exam Tip
पहला पद (4) और अंतर (5) है, इसलिए \(a_n=5n-1\) है। परीक्षा में (n=1) रखकर पहला पद जरूर जाँचें।
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अनुक्रम \(42,37,32,27,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(42,37,32,27,\ldots\)?
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A \(a_n=42-5n\)
B \(a_n=47-5n\)
C \(a_n=5n+37\)
D \(a_n=47+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=47-5n\)
Step 1
Concept
At (n=1) it gives (42), and at (n=2) it gives (37), so \(a_n=47-5n\). In exams, always match the first term in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=47-5n\). At (n=1) it gives (42), and at (n=2) it gives (37), so \(a_n=47-5n\). In exams, always match the first term in a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (42) और (n=2) पर (37) मिलता है, इसलिए \(a_n=47-5n\) है। परीक्षा में घटते अनुक्रम में पहला पद जरूर मिलाएँ।
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यदि \(a_n=3n+2\) है, तो कौन-सा पद (38) के बराबर होगा?
If \(a_n=3n+2\), which term will be equal to (38)?
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A (n=9)
B (n=10)
C (n=11)
D (n=12)
Explanation opens after your attempt
Step 1
Concept
From (3n+2=38), we get (n=12). 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 D. (n=12). From (3n+2=38), we get (n=12). In exams, equate the formula to the given value when term number is asked.
Step 3
Exam Tip
(3n+2=38) से (n=12) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(5,8,11,14,\ldots\) में (32) कौन-सा पद है?
In the sequence \(5,8,11,14,\ldots\), which term is (32)?
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A आठवाँ पद / (8)th term
B नौवाँ पद / (9)th term
C दसवाँ पद / (10)th term
D ग्यारहवाँ पद / (11)th term
Explanation opens after your attempt
Correct Answer
C. दसवाँ पद / (10)th term
Step 1
Concept
Its rule is \(a_n=3n+2\), and (3n+2=32) gives (n=10). In exams, form the general term first to find the term number.
Step 2
Why this answer is correct
The correct answer is C. दसवाँ पद / (10)th term. Its rule is \(a_n=3n+2\), and (3n+2=32) gives (n=10). 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=32) से (n=10) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।
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अनुक्रम \(4,9,16,25,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,9,16,25,\ldots\)?
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A (a_n=(n+1)2 )
B \(a_n=n^2\)
C \(a_n=n^2+1\)
D \(a_n=2n^2\)
Explanation opens after your attempt
Correct Answer
A. (a_n=(n+1)2 )
Step 1
Concept
These terms are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)2 ). In exams, recognize shifted square numbers.
Step 2
Why this answer is correct
The correct answer is A. (a_n=(n+1)2 ). These terms are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)2 ). In exams, recognize shifted square numbers.
Step 3
Exam Tip
ये पद \(2^2,3^2,4^2,5^2\) हैं, इसलिए (a_n=(n+1)2 ) है। परीक्षा में वर्ग संख्याओं के स्थानांतरण को पहचानें।
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अनुक्रम \(2,6,12,20,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,6,12,20,\ldots\)?
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A \(a_n=n^2+1\)
B \(a_n=2n\)
C \(a_n=n^2+n+1\)
D (a_n=n(n+1))
Explanation opens after your attempt
Correct Answer
D. (a_n=n(n+1))
Step 1
Concept
(n(n+1)) gives (2,6,12,20). In exams, check rules involving the product of consecutive numbers.
Step 2
Why this answer is correct
The correct answer is D. (a_n=n(n+1)). (n(n+1)) gives (2,6,12,20). In exams, check rules involving the product of consecutive numbers.
Step 3
Exam Tip
(n(n+1)) से (2,6,12,20) मिलते हैं। परीक्षा में लगातार दो संख्याओं के गुणन वाले नियम को जाँचें।
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अनुक्रम \(2,4,7,11,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,4,7,11,\ldots\)?
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A (a_n=\frac{n(n-1)}{2})
B \(a_n=n^2+1\)
C (a_n=\frac{n(n+1)}{2}+1)
D \(a_n=2n\)
Explanation opens after your attempt
Correct Answer
C. (a_n=\frac{n(n+1)}{2}+1)
Step 1
Concept
Adding (1) to triangular numbers gives (2,4,7,11). In exams, think of triangular numbers when differences are (2,3,4).
Step 2
Why this answer is correct
The correct answer is C. (a_n=\frac{n(n+1)}{2}+1). Adding (1) to triangular numbers gives (2,4,7,11). In exams, think of triangular numbers when differences are (2,3,4).
Step 3
Exam Tip
त्रिभुज संख्या में (1) जोड़ने से (2,4,7,11) मिलते हैं। परीक्षा में अंतर (2,3,4) दिखे तो त्रिभुज संख्या सोचें।
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अनुक्रम \(0,3,8,15,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(0,3,8,15,\ldots\)?
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A \(a_n=n^2-1\)
B \(a_n=n^2+1\)
C \(a_n=2n-2\)
D (a_n=n(n+1))
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-1\)
Step 1
Concept
\(n^2-1\) gives (0,3,8,15). In exams, match by subtracting (1) from square numbers.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-1\). \(n^2-1\) gives (0,3,8,15). In exams, match by subtracting (1) from square numbers.
Step 3
Exam Tip
\(n^2-1\) से (0,3,8,15) मिलते हैं। परीक्षा में वर्ग संख्याओं से (1) घटाकर मिलान करें।
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यदि \(a_n=n^2-1\) है, तो कौन-सा पद (35) के बराबर होगा?
If \(a_n=n^2-1\), which term will be equal to (35)?
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A (n=4)
B (n=5)
C (n=7)
D (n=6)
Explanation opens after your attempt
Step 1
Concept
From \(n^2-1=35\), we get \(n^2=36\) and (n=6). In exams, complete the square value to find the term number.
Step 2
Why this answer is correct
The correct answer is D. (n=6). From \(n^2-1=35\), we get \(n^2=36\) and (n=6). In exams, complete the square value to find the term number.
Step 3
Exam Tip
\(n^2-1=35\) से \(n^2=36\) और (n=6) मिलता है। परीक्षा में वर्ग पूरा करके पद संख्या निकालें।
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अनुक्रम \(5,11,29,83,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,11,29,83,\ldots\)?
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A \(a_n=3n+2\)
B \(a_n=3^n+2\)
C \(a_n=3^n-2\)
D \(a_n=n^3+4\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3^n+2\)
Step 1
Concept
\(3^n+2\) gives (5,11,29,83). In exams, check powers in rapidly increasing sequences.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3^n+2\). \(3^n+2\) gives (5,11,29,83). In exams, check powers in rapidly increasing sequences.
Step 3
Exam Tip
\(3^n+2\) से (5,11,29,83) मिलते हैं। परीक्षा में तेज वृद्धि वाले अनुक्रमों में घात जाँचें।
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अनुक्रम \(6,18,54,162,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(6,18,54,162,\ldots\)?
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A \(a_n=6n\)
B \(a_n=3^n+3\)
C \(a_n=2\cdot3^n\)
D \(a_n=6\cdot2^{n-1}\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=2\cdot3^n\)
Step 1
Concept
\(2\cdot3^n\) gives (6,18,54,162). In exams, check powers of the base for geometric growth.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=2\cdot3^n\). \(2\cdot3^n\) gives (6,18,54,162). In exams, check powers of the base for geometric growth.
Step 3
Exam Tip
\(2\cdot3^n\) से (6,18,54,162) मिलते हैं। परीक्षा में गुणोत्तर वृद्धि के लिए आधार की घात जाँचें।
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अनुक्रम \(5,10,20,40,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,10,20,40,\ldots\)?
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A \(a_n=5\cdot2^{n-1}\)
B \(a_n=5n\)
C \(a_n=2^n+3\)
D \(a_n=10n-5\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5\cdot2^{n-1}\)
Step 1
Concept
The first term is (5), and each term is multiplied by (2). In exams, check both the first term and ratio in a geometric sequence.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5\cdot2^{n-1}\). The first term is (5), and each term is multiplied by (2). In exams, check both the first term and ratio in a geometric sequence.
Step 3
Exam Tip
पहला पद (5) है और हर बार (2) से गुणा हो रहा है। परीक्षा में गुणोत्तर अनुक्रम में पहले पद और अनुपात दोनों देखें।
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अनुक्रम \(2,10,24,44,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,10,24,44,\ldots\)?
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A \(a_n=2n^2\)
B \(a_n=3n^2-n\)
C \(a_n=n^2+n\)
D \(a_n=4n^2-2n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3n^2-n\)
Step 1
Concept
\(3n^2-n\) gives (2,10,24,44). In exams, match polynomial rules using small (n) values.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3n^2-n\). \(3n^2-n\) gives (2,10,24,44). In exams, match polynomial rules using small (n) values.
Step 3
Exam Tip
\(3n^2-n\) से (2,10,24,44) मिलते हैं। परीक्षा में बहुपद नियमों को छोटे (n) मानों से मिलाएँ।
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अनुक्रम \(2,10,30,68,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,10,30,68,\ldots\)?
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A \(a_n=n^3+n\)
B \(a_n=n^2+n\)
C \(a_n=2n^3\)
D \(a_n=n^3+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^3+n\)
Step 1
Concept
\(n^3+n\) gives (2,10,30,68). In exams, test the cube-based rule on the first three terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^3+n\). \(n^3+n\) gives (2,10,30,68). In exams, test the cube-based rule on the first three terms.
Step 3
Exam Tip
\(n^3+n\) से (2,10,30,68) मिलते हैं। परीक्षा में घन वाले नियम को पहले तीन पदों पर जाँचें।
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यदि \(a_n=2n-1\) है, तो कौन-सा पद (41) के बराबर होगा?
If \(a_n=2n-1\), which term will be equal to (41)?
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A (n=18)
B (n=19)
C (n=20)
D (n=21)
Explanation opens after your attempt
Step 1
Concept
From (2n-1=41), we get (n=21). In exams, find the term number of an odd number using the formula.
Step 2
Why this answer is correct
The correct answer is D. (n=21). From (2n-1=41), we get (n=21). In exams, find the term number of an odd number using the formula.
Step 3
Exam Tip
(2n-1=41) से (n=21) मिलता है। परीक्षा में विषम संख्या के पद को सूत्र से निकालें।
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अनुक्रम \(7,10,13,16,\ldots\) में (58) कौन-सा पद है?
In the sequence \(7,10,13,16,\ldots\), which term is (58)?
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A सत्रहवाँ पद / (17)th term
B अठारहवाँ पद / (18)th term
C उन्नीसवाँ पद / (19)th term
D बीसवाँ पद / (20)th term
Explanation opens after your attempt
Correct Answer
B. अठारहवाँ पद / (18)th term
Step 1
Concept
Its rule is \(a_n=3n+4\), and (3n+4=58) gives (n=18). In exams, write the rule first and compare it with the given term.
Step 2
Why this answer is correct
The correct answer is B. अठारहवाँ पद / (18)th term. Its rule is \(a_n=3n+4\), and (3n+4=58) gives (n=18). In exams, write the rule first and compare it with the given term.
Step 3
Exam Tip
इसका नियम \(a_n=3n+4\) है और (3n+4=58) से (n=18) है। परीक्षा में पहले नियम लिखकर दिए पद से तुलना करें।
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अनुक्रम \(8,14,20,26,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(8,14,20,26,\ldots\)?
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A \(a_n=8n\)
B \(a_n=6n-2\)
C \(a_n=6n+2\)
D \(a_n=2n+6\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=6n+2\)
Step 1
Concept
The difference is (6) and the first term is (8), so \(a_n=6n+2\). In exams, find the constant to match the first term.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=6n+2\). The difference is (6) and the first term is (8), so \(a_n=6n+2\). In exams, find the constant to match the first term.
Step 3
Exam Tip
अंतर (6) है और पहला पद (8) है, इसलिए \(a_n=6n+2\) है। परीक्षा में पहला पद मिलाने के लिए स्थिर संख्या निकालें।
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यदि \(a_n=6n+2\) है, तो पहले तीन पदों का योग क्या होगा?
If \(a_n=6n+2\), what is the sum of the first three terms?
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A (42)
B (40)
C (44)
D (46)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (8,14,20), and their sum is (42). In exams, find all required terms when a sum is asked.
Step 2
Why this answer is correct
The correct answer is A. (42). The first three terms are (8,14,20), and their sum is (42). In exams, find all required terms when a sum is asked.
Step 3
Exam Tip
पहले तीन पद (8,14,20) हैं और योग (42) है। परीक्षा में योग पूछे जाने पर सभी आवश्यक पद निकालें।
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अनुक्रम \(1,5,11,19,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,5,11,19,\ldots\)?
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A \(a_n=n^2+1\)
B \(a_n=2n^2-1\)
C \(a_n=n^2+n-1\)
D \(a_n=n^2+2n\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=n^2+n-1\)
Step 1
Concept
\(n^2+n-1\) gives (1,5,11,19). In exams, check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=n^2+n-1\). \(n^2+n-1\) gives (1,5,11,19). In exams, check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(n^2+n-1\) से (1,5,11,19) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें।
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अनुक्रम \(2,\frac{7}{2},5,\frac{13}{2},\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,\frac{7}{2},5,\frac{13}{2},\ldots\)?
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#class-9
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A \(a_n=\frac{n+3}{2}\)
B \(a_n=\frac{3n+1}{2}\)
C \(a_n=\frac{2n+3}{2}\)
D \(a_n=2n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{3n+1}{2}\)
Step 1
Concept
\(\frac{3n+1}{2}\) gives \(2,\frac{7}{2},5,\frac{13}{2}\). In exams, match fractional terms using small (n) values.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{3n+1}{2}\). \(\frac{3n+1}{2}\) gives \(2,\frac{7}{2},5,\frac{13}{2}\). In exams, match fractional terms using small (n) values.
Step 3
Exam Tip
\(\frac{3n+1}{2}\) से \(2,\frac{7}{2},5,\frac{13}{2}\) मिलते हैं। परीक्षा में भिन्न पदों को छोटे (n) मानों से मिलाएँ।
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यदि (a_n=\frac{n(n+1)}{2}) है, तो कौन-सा पद (28) के बराबर होगा?
If (a_n=\frac{n(n+1)}{2}), which term will be equal to (28)?
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A (n=5)
B (n=6)
C (n=8)
D (n=7)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7\times8}{2}=28\), so (n=7). In exams, remembering triangular numbers is useful.
Step 2
Why this answer is correct
The correct answer is D. (n=7). \(\frac{7\times8}{2}=28\), so (n=7). In exams, remembering triangular numbers is useful.
Step 3
Exam Tip
\(\frac{7\times8}{2}=28\), इसलिए (n=7) है। परीक्षा में त्रिभुज संख्याओं को याद रखना उपयोगी है।
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अनुक्रम \(3,6,11,20,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,6,11,20,\ldots\)?
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A \(a_n=2^n+n\)
B \(a_n=2n+1\)
C \(a_n=n^2+2\)
D \(a_n=3n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2^n+n\)
Step 1
Concept
\(2^n+n\) gives (3,6,11,20). In exams, also check the extra (n) in power-based rules.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2^n+n\). \(2^n+n\) gives (3,6,11,20). In exams, also check the extra (n) in power-based rules.
Step 3
Exam Tip
\(2^n+n\) से (3,6,11,20) मिलते हैं। परीक्षा में घात वाले नियमों में अतिरिक्त (n) भी जाँचें।
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यदि \(a_n=2n^2+2n\) है, तो कौन-सा पद (60) के बराबर होगा?
If \(a_n=2n^2+2n\), which term will be equal to (60)?
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A (n=4)
B (n=6)
C (n=5)
D (n=7)
Explanation opens after your attempt
Step 1
Concept
Putting (n=5) in \(2n^2+2n=60\) gives (60). In exams, you can also check quickly by substituting options.
Step 2
Why this answer is correct
The correct answer is C. (n=5). Putting (n=5) in \(2n^2+2n=60\) gives (60). In exams, you can also check quickly by substituting options.
Step 3
Exam Tip
\(2n^2+2n=60\) में (n=5) रखने पर मान (60) मिलता है। परीक्षा में विकल्पों को रखकर भी जल्दी जाँच सकते हैं।
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अनुक्रम \(4,12,24,40,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,12,24,40,\ldots\)?
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A \(a_n=4n\)
B \(a_n=2n^2+2n\)
C \(a_n=n^2+3n\)
D \(a_n=2n^2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=2n^2+2n\)
Step 1
Concept
\(2n^2+2n\) gives (4,12,24,40). In exams, check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=2n^2+2n\). \(2n^2+2n\) gives (4,12,24,40). In exams, check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(2n^2+2n\) से (4,12,24,40) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें।
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