अनुक्रम \(6,10,14,18,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(6,10,14,18,\ldots\)?
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A \(a_n=4n\)
B \(a_n=6n-2\)
C \(a_n=4n+2\)
D \(a_n=n+5\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=4n+2\)
Step 1
Concept
The first term is (6) and the difference is (4) so \(a_n=4n+2\). In exams check the first term by putting (n=1).
Step 2
Why this answer is correct
The correct answer is C. \(a_n=4n+2\). The first term is (6) and the difference is (4) so \(a_n=4n+2\). In exams check the first term by putting (n=1).
Step 3
Exam Tip
पहला पद (6) और अंतर (4) है इसलिए \(a_n=4n+2\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।
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अनुक्रम \(47,43,39,35,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(47,43,39,35,\ldots\)?
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A \(a_n=47-4n\)
B \(a_n=4n+43\)
C \(a_n=51-4n\)
D \(a_n=51+n\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=51-4n\)
Step 1
Concept
At (n=1) it gives (47) and at (n=2) it gives (43) so \(a_n=51-4n\). In exams match the first term in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=51-4n\). At (n=1) it gives (47) and at (n=2) it gives (43) so \(a_n=51-4n\). In exams match the first term in a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (47) और (n=2) पर (43) मिलता है इसलिए \(a_n=51-4n\) है। परीक्षा में घटते अनुक्रम में पहला पद मिलाएँ।
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यदि \(a_n=5n+4\) है तो कौन-सा पद (64) के बराबर होगा?
If \(a_n=5n+4\) then which term is equal to (64)?
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A (n=12)
B (n=11)
C (n=13)
D (n=10)
Explanation opens after your attempt
Step 1
Concept
From (5n+4=64) we get (n=12). In exams equate the formula to the given value to find the term number.
Step 2
Why this answer is correct
The correct answer is A. (n=12). From (5n+4=64) we get (n=12). In exams equate the formula to the given value to find the term number.
Step 3
Exam Tip
(5n+4=64) से (n=12) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(2,5,8,11,\ldots\) में (38) कौन-सा पद है?
In the sequence \(2,5,8,11,\ldots\) which term is (38)?
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A दसवाँ पद / (10)th term
B ग्यारहवाँ पद / (11)th term
C बारहवाँ पद / (12)th term
D तेरहवाँ पद / (13)th term
Explanation opens after your attempt
Correct Answer
D. तेरहवाँ पद / (13)th term
Step 1
Concept
Its rule is \(a_n=3n-1\) and (3n-1=38) gives (n=13). In exams form the general term first to find the term number.
Step 2
Why this answer is correct
The correct answer is D. तेरहवाँ पद / (13)th term. Its rule is \(a_n=3n-1\) and (3n-1=38) gives (n=13). In exams form the general term first to find the term number.
Step 3
Exam Tip
इसका नियम \(a_n=3n-1\) है और (3n-1=38) से (n=13) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।
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अनुक्रम \(9,16,25,36,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(9,16,25,36,\ldots\)?
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A \(a_n=n^2\)
B (a_n=(n+2)2 )
C \(a_n=n^2+2\)
D \(a_n=3n^2\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(n+2)2 )
Step 1
Concept
These terms are \(3^2,4^2,5^2,6^2\) so (a_n=(n+2)2 ). In exams recognize shifted square numbers.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(n+2)2 ). These terms are \(3^2,4^2,5^2,6^2\) so (a_n=(n+2)2 ). In exams recognize shifted square numbers.
Step 3
Exam Tip
ये पद \(3^2,4^2,5^2,6^2\) हैं इसलिए (a_n=(n+2)2 ) है। परीक्षा में स्थानांतरित वर्ग संख्याएँ पहचानें।
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अनुक्रम \(1,4,9,16,\ldots\) में (81) कौन-सा पद है?
In the sequence \(1,4,9,16,\ldots\) which term is (81)?
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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 \(a_n=n^2\) and \(n^2=81\) gives (n=9). In exams identify the term number of square numbers.
Step 2
Why this answer is correct
The correct answer is C. नौवाँ पद / (9)th term. Its rule is \(a_n=n^2\) and \(n^2=81\) gives (n=9). In exams identify the term number of square numbers.
Step 3
Exam Tip
इसका नियम \(a_n=n^2\) है और \(n^2=81\) से (n=9) है। परीक्षा में वर्ग संख्याओं की पद संख्या पहचानें।
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अनुक्रम \(3,5,8,12,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,5,8,12,\ldots\)?
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A \(a_n=n^2+2\)
B (a_n=\frac{n(n+1)}{2}+2)
C \(a_n=2n+1\)
D (a_n=\frac{n(n+3)}{2})
Explanation opens after your attempt
Correct Answer
B. (a_n=\frac{n(n+1)}{2}+2)
Step 1
Concept
(\frac{n(n+1)}{2}+2) gives (3,5,8,12). In exams think of triangular numbers when differences are (2,3,4).
Step 2
Why this answer is correct
The correct answer is B. (a_n=\frac{n(n+1)}{2}+2). (\frac{n(n+1)}{2}+2) gives (3,5,8,12). In exams think of triangular numbers when differences are (2,3,4).
Step 3
Exam Tip
(\frac{n(n+1)}{2}+2) से (3,5,8,12) मिलते हैं। परीक्षा में बढ़ते अंतर (2,3,4) देखकर त्रिभुज संख्या सोचें।
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अनुक्रम \(0,5,12,21,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(0,5,12,21,\ldots\)?
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A \(a_n=n^2-1\)
B \(a_n=n^2+n-2\)
C \(a_n=2n^2-2\)
D \(a_n=5n-5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+n-2\)
Step 1
Concept
\(n^2+n-2\) gives (0,5,12,21). In exams test a quadratic rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+n-2\). \(n^2+n-2\) gives (0,5,12,21). In exams test a quadratic rule on the first four terms.
Step 3
Exam Tip
\(n^2+n-2\) से (0,5,12,21) मिलते हैं। परीक्षा में वर्गीय नियम को पहले चार पदों पर जाँचें।
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यदि \(a_n=n^2+n-2\) है तो कौन-सा पद (70) के बराबर होगा?
If \(a_n=n^2+n-2\) then which term is equal to (70)?
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A (n=7)
B (n=8)
C (n=9)
D (n=10)
Explanation opens after your attempt
Step 1
Concept
\(8^2+8-2=70\) so (n=8). In exams you can check quickly by substituting options.
Step 2
Why this answer is correct
The correct answer is B. (n=8). \(8^2+8-2=70\) so (n=8). In exams you can check quickly by substituting options.
Step 3
Exam Tip
\(8^2+8-2=70\) है इसलिए (n=8) है। परीक्षा में विकल्प रखकर भी जल्दी जाँच सकते हैं।
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अनुक्रम \(4,10,28,82,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,10,28,82,\ldots\)?
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A \(a_n=3^n+1\)
B \(a_n=3n+1\)
C \(a_n=2^n+2n\)
D \(a_n=n^3+3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3^n+1\)
Step 1
Concept
\(3^n+1\) gives (4,10,28,82). In exams match power-based options with the first terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3^n+1\). \(3^n+1\) gives (4,10,28,82). In exams match power-based options with the first terms.
Step 3
Exam Tip
\(3^n+1\) से (4,10,28,82) मिलते हैं। परीक्षा में घात वाले विकल्पों को पहले पदों से मिलाएँ।
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अनुक्रम \(12,24,48,96,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(12,24,48,96,\ldots\)?
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A \(a_n=12n\)
B \(a_n=6\cdot2^n\)
C \(a_n=12\cdot2^n\)
D \(a_n=2n+10\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=6\cdot2^n\)
Step 1
Concept
\(6\cdot2^n\) gives (12,24,48,96). In exams check both the base and multiplier in geometric growth.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=6\cdot2^n\). \(6\cdot2^n\) gives (12,24,48,96). In exams check both the base and multiplier in geometric growth.
Step 3
Exam Tip
\(6\cdot2^n\) से (12,24,48,96) मिलते हैं। परीक्षा में गुणोत्तर वृद्धि में आधार और गुणक दोनों जाँचें।
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अनुक्रम \(3,6,12,24,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,6,12,24,\ldots\)?
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A \(a_n=3n\)
B \(a_n=2^n+1\)
C \(a_n=3\cdot2^n\)
D \(a_n=3\cdot2^{n-1}\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=3\cdot2^{n-1}\)
Step 1
Concept
The first term is (3) and each term is multiplied by (2) so \(a_n=3\cdot2^{n-1}\). In exams check both the first term and ratio.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=3\cdot2^{n-1}\). The first term is (3) and each term is multiplied by (2) so \(a_n=3\cdot2^{n-1}\). In exams check both the first term and ratio.
Step 3
Exam Tip
पहला पद (3) है और हर बार (2) से गुणा हो रहा है इसलिए \(a_n=3\cdot2^{n-1}\) है। परीक्षा में पहले पद और अनुपात दोनों देखें।
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अनुक्रम \(4,15,32,55,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,15,32,55,\ldots\)?
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A \(a_n=3n^2+2n-1\)
B \(a_n=4n\)
C \(a_n=5n^2-1\)
D \(a_n=11n-7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+2n-1\)
Step 1
Concept
\(3n^2+2n-1\) gives (4,15,32,55). In exams test options with small values of (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+2n-1\). \(3n^2+2n-1\) gives (4,15,32,55). In exams test options with small values of (n).
Step 3
Exam Tip
\(3n^2+2n-1\) से (4,15,32,55) मिलते हैं। परीक्षा में विकल्पों को छोटे (n) मानों से जाँचें।
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यदि \(a_n=2n^2+3n\) है तो पहले तीन पदों का योग क्या होगा?
If \(a_n=2n^2+3n\) then what is the sum of the first three terms?
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A (42)
B (44)
C (46)
D (48)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (5,14,27) and the sum is (46). In exams write all terms before adding.
Step 2
Why this answer is correct
The correct answer is A. (42). The first three terms are (5,14,27) and the sum is (46). In exams write all terms before adding.
Step 3
Exam Tip
पहले तीन पद (5,14,27) हैं और योग (46) नहीं बल्कि (46) है। परीक्षा में योग से पहले सभी पद लिखें।
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अनुक्रम \(2,8,14,20,\ldots\) में (68) कौन-सा पद है?
In the sequence \(2,8,14,20,\ldots\) which term is (68)?
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A दसवाँ पद / (10)th term
B ग्यारहवाँ पद / (11)th term
C बारहवाँ पद / (12)th term
D तेरहवाँ पद / (13)th term
Explanation opens after your attempt
Correct Answer
C. बारहवाँ पद / (12)th term
Step 1
Concept
Its rule is \(a_n=6n-4\) and (6n-4=68) gives (n=12). In exams equate the given term to the general term.
Step 2
Why this answer is correct
The correct answer is C. बारहवाँ पद / (12)th term. Its rule is \(a_n=6n-4\) and (6n-4=68) gives (n=12). In exams equate the given term to the general term.
Step 3
Exam Tip
इसका नियम \(a_n=6n-4\) है और (6n-4=68) से (n=12) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।
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अनुक्रम \(1,\frac{7}{5},\frac{9}{5},\frac{11}{5},\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,\frac{7}{5},\frac{9}{5},\frac{11}{5},\ldots\)?
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A \(a_n=\frac{n+4}{5}\)
B \(a_n=\frac{2n+3}{5}\)
C \(a_n=\frac{5n+2}{3}\)
D \(a_n=2n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{2n+3}{5}\)
Step 1
Concept
\(\frac{2n+3}{5}\) gives the given terms. In exams match fractional terms using small values of (n).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{2n+3}{5}\). \(\frac{2n+3}{5}\) gives the given terms. In exams match fractional terms using small values of (n).
Step 3
Exam Tip
\(\frac{2n+3}{5}\) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को छोटे (n) मानों से मिलाएँ।
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अनुक्रम \(11,21,31,41,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(11,21,31,41,\ldots\)?
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A \(a_n=11n\)
B \(a_n=10n+1\)
C \(a_n=n+10\)
D \(a_n=10n-1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=10n+1\)
Step 1
Concept
The first term is (11) and the difference is (10) so \(a_n=10n+1\). In exams find the constant part from the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=10n+1\). The first term is (11) and the difference is (10) so \(a_n=10n+1\). In exams find the constant part from the first term.
Step 3
Exam Tip
पहला पद (11) और अंतर (10) है इसलिए \(a_n=10n+1\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।
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अनुक्रम \(5,17,37,65,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(5,17,37,65,\ldots\)?
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A \(a_n=4n+1\)
B \(a_n=4n^2+1\)
C \(a_n=5n^2\)
D \(a_n=12n-7\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n^2+1\)
Step 1
Concept
\(4n^2+1\) gives (5,17,37,65). In exams check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n^2+1\). \(4n^2+1\) gives (5,17,37,65). In exams check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(4n^2+1\) से (5,17,37,65) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम जाँचें।
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अनुक्रम \(1,2,5,12,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,2,5,12,\ldots\)?
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A \(a_n=2^n-n\)
B \(a_n=2n-1\)
C \(a_n=n^2\)
D \(a_n=2^n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2^n-n\)
Step 1
Concept
\(2^n-n\) gives (1,2,5,12). In exams also check subtraction of the term number 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 (1,2,5,12). In exams also check subtraction of the term number in power-based rules.
Step 3
Exam Tip
\(2^n-n\) से (1,2,5,12) मिलते हैं। परीक्षा में घात वाले नियम में पद संख्या घटाना भी जाँचें।
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यदि \(a_n=n^3-1\) है तो कौन-सा पद (124) के बराबर होगा?
If \(a_n=n^3-1\) then which term is equal to (124)?
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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 \(n^3-1=124\) we get \(n^3=125\) and (n=5). In exams recognize cube numbers.
Step 2
Why this answer is correct
The correct answer is B. (n=5). From \(n^3-1=124\) we get \(n^3=125\) and (n=5). In exams recognize cube numbers.
Step 3
Exam Tip
\(n^3-1=124\) से \(n^3=125\) और (n=5) है। परीक्षा में घन संख्या पहचानें।
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अनुक्रम \(0,7,26,63,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(0,7,26,63,\ldots\)?
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#explicit-rule
#class-9
#medium
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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 rules 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 rules with the first four terms.
Step 3
Exam Tip
\(n^3-1\) से (0,7,26,63) मिलते हैं। परीक्षा में घन वाले नियम को पहले चार पदों से मिलाएँ।
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अनुक्रम \(3,18,57,132,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(3,18,57,132,\ldots\)?
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A \(a_n=2n^3+n\)
B \(a_n=3n^2\)
C \(a_n=2n^2+n\)
D \(a_n=n^3+2n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2n^3+n\)
Step 1
Concept
\(2n^3+n\) gives (3,18,57,132). In exams test cube-based options with small (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2n^3+n\). \(2n^3+n\) gives (3,18,57,132). In exams test cube-based options with small (n).
Step 3
Exam Tip
\(2n^3+n\) से (3,18,57,132) मिलते हैं। परीक्षा में घन आधारित विकल्पों को छोटे (n) से जाँचें।
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अनुक्रम \(74,68,62,56,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(74,68,62,56,\ldots\)?
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A \(a_n=74-6n\)
B \(a_n=80-6n\)
C \(a_n=6n+68\)
D \(a_n=80+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=80-6n\)
Step 1
Concept
At (n=1) it gives (74) and at (n=2) it gives (68) so \(a_n=80-6n\). In exams check the first two terms of a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=80-6n\). At (n=1) it gives (74) and at (n=2) it gives (68) so \(a_n=80-6n\). In exams check the first two terms of a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (74) और (n=2) पर (68) मिलता है इसलिए \(a_n=80-6n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें।
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अनुक्रम \(5,14,27,44,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,14,27,44,\ldots\)?
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A \(a_n=n^2+4n\)
B \(a_n=5n\)
C \(a_n=3n^2+2\)
D \(a_n=2n^2+3n\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=2n^2+3n\)
Step 1
Concept
\(2n^2+3n\) gives (5,14,27,44). In exams test the rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=2n^2+3n\). \(2n^2+3n\) gives (5,14,27,44). In exams test the rule on the first four terms.
Step 3
Exam Tip
\(2n^2+3n\) से (5,14,27,44) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।
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