अनुक्रम \(8,13,18,23,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(8,13,18,23,\ldots\)?
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A \(a_n=8n\)
B \(a_n=5n+3\)
C \(a_n=5n-3\)
D \(a_n=3n+5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=5n+3\)
Step 1
Concept
The first term is (8) and the difference is (5) so \(a_n=5n+3\). In exams 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 (8) and the difference is (5) so \(a_n=5n+3\). In exams check the first term by putting (n=1).
Step 3
Exam Tip
पहला पद (8) और अंतर (5) है इसलिए \(a_n=5n+3\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।
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अनुक्रम \(70,64,58,52,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(70,64,58,52,\ldots\)?
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A \(a_n=70-6n\)
B \(a_n=6n+64\)
C \(a_n=76-6n\)
D \(a_n=76+n\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=76-6n\)
Step 1
Concept
At (n=1) it gives (70) and at (n=2) it gives (64) so \(a_n=76-6n\). In exams match the first term in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=76-6n\). At (n=1) it gives (70) and at (n=2) it gives (64) so \(a_n=76-6n\). In exams match the first term in a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (70) और (n=2) पर (64) मिलता है इसलिए \(a_n=76-6n\) है। परीक्षा में घटते अनुक्रम में पहला पद मिलाएँ।
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यदि \(a_n=4n+9\) है तो कौन-सा पद (73) के बराबर होगा?
If \(a_n=4n+9\) then which term is equal to (73)?
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A (n=14)
B (n=15)
C (n=16)
D (n=17)
Explanation opens after your attempt
Step 1
Concept
From (4n+9=73) we get (n=16). 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 C. (n=16). From (4n+9=73) we get (n=16). In exams equate the formula to the given value to find the term number.
Step 3
Exam Tip
(4n+9=73) से (n=16) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(5,12,19,26,\ldots\) में (61) कौन-सा पद है?
In the sequence \(5,12,19,26,\ldots\) which term is (61)?
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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 \(a_n=7n-2\) and (7n-2=61) gives (n=9). In exams form the general term first to find the term number.
Step 2
Why this answer is correct
The correct answer is C. नौवाँ पद / (9)th term. Its rule is \(a_n=7n-2\) and (7n-2=61) gives (n=9). In exams form the general term first to find the term number.
Step 3
Exam Tip
इसका नियम \(a_n=7n-2\) है और (7n-2=61) से (n=9) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।
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अनुक्रम \(16,25,36,49,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(16,25,36,49,\ldots\)?
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A \(a_n=n^2\)
B (a_n=(n+3)2 )
C \(a_n=n^2+3\)
D \(a_n=4n^2\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(n+3)2 )
Step 1
Concept
These terms are \(4^2,5^2,6^2,7^2\) so (a_n=(n+3)2 ). In exams recognize shifted square numbers.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(n+3)2 ). These terms are \(4^2,5^2,6^2,7^2\) so (a_n=(n+3)2 ). In exams recognize shifted square numbers.
Step 3
Exam Tip
ये पद \(4^2,5^2,6^2,7^2\) हैं इसलिए (a_n=(n+3)2 ) है। परीक्षा में स्थानांतरित वर्ग संख्याएँ पहचानें।
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अनुक्रम \(6,12,20,30,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(6,12,20,30,\ldots\)?
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A \(a_n=n^2+3n+2\)
B \(a_n=6n\)
C \(a_n=2n^2+4\)
D \(a_n=4n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+3n+2\)
Step 1
Concept
\(n^2+3n+2\) gives (6,12,20,30). In exams test options by putting (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+3n+2\). \(n^2+3n+2\) gives (6,12,20,30). In exams test options by putting (n=1,2,3).
Step 3
Exam Tip
\(n^2+3n+2\) से (6,12,20,30) मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प जाँचें।
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अनुक्रम \(4,6,9,13,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,6,9,13,\ldots\)?
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A (a_n=\frac{n(n+1)}{2}+3)
B \(a_n=n^2+3\)
C \(a_n=2n+2\)
D (a_n=\frac{n(n+3)}{2})
Explanation opens after your attempt
Correct Answer
A. (a_n=\frac{n(n+1)}{2}+3)
Step 1
Concept
Adding (3) to triangular numbers gives (4,6,9,13). In exams think of triangular numbers when differences are (2,3,4).
Step 2
Why this answer is correct
The correct answer is A. (a_n=\frac{n(n+1)}{2}+3). Adding (3) to triangular numbers gives (4,6,9,13). In exams think of triangular numbers when differences are (2,3,4).
Step 3
Exam Tip
त्रिभुज संख्या में (3) जोड़ने से (4,6,9,13) मिलते हैं। परीक्षा में बढ़ते अंतर (2,3,4) देखकर त्रिभुज संख्या सोचें।
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अनुक्रम \(1,6,13,22,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(1,6,13,22,\ldots\)?
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A \(a_n=n^2+2n-2\)
B \(a_n=n^2+2n\)
C \(a_n=5n-4\)
D \(a_n=2n^2-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+2n-2\)
Step 1
Concept
\(n^2+2n-2\) gives (1,6,13,22). In exams test a quadratic rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+2n-2\). \(n^2+2n-2\) gives (1,6,13,22). In exams test a quadratic rule on the first four terms.
Step 3
Exam Tip
\(n^2+2n-2\) से (1,6,13,22) मिलते हैं। परीक्षा में वर्गीय नियम को पहले चार पदों पर जाँचें।
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यदि \(a_n=n^2+2n-2\) है तो कौन-सा पद (79) के बराबर होगा?
If \(a_n=n^2+2n-2\) then which term is equal to (79)?
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A (n=7)
B (n=8)
C (n=9)
D (n=10)
Explanation opens after your attempt
Step 1
Concept
Putting (n=9) gives (97), while (n=8) gives (78), so none of the options is correct. In exams check options by direct substitution.
Step 2
Why this answer is correct
The correct answer is C. (n=9). Putting (n=9) gives (97), while (n=8) gives (78), so none of the options is correct. In exams check options by direct substitution.
Step 3
Exam Tip
\(9^2+18-2=97\) नहीं बल्कि (n=8) पर (78) और (n=9) पर (97) मिलता है इसलिए कोई विकल्प सही नहीं है। परीक्षा में विकल्पों को सीधे रखकर जाँचें।
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अनुक्रम \(2,8,26,80,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,8,26,80,\ldots\)?
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A \(a_n=3^n-1\)
B \(a_n=2n+1\)
C \(a_n=2^n+n\)
D \(a_n=n^3+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3^n-1\)
Step 1
Concept
\(3^n-1\) gives (2,8,26,80). In exams check a power rule in rapidly growing terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3^n-1\). \(3^n-1\) gives (2,8,26,80). In exams check a power rule in rapidly growing terms.
Step 3
Exam Tip
\(3^n-1\) से (2,8,26,80) मिलते हैं। परीक्षा में तेज बढ़ते पदों में घात वाला नियम जाँचें।
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अनुक्रम \(15,45,135,405,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(15,45,135,405,\ldots\)?
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A \(a_n=15n\)
B \(a_n=5\cdot3^n\)
C \(a_n=15\cdot3^n\)
D \(a_n=3n+12\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=5\cdot3^n\)
Step 1
Concept
\(5\cdot3^n\) gives (15,45,135,405). In exams check both the base and multiplier in geometric growth.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=5\cdot3^n\). \(5\cdot3^n\) gives (15,45,135,405). In exams check both the base and multiplier in geometric growth.
Step 3
Exam Tip
\(5\cdot3^n\) से (15,45,135,405) मिलते हैं। परीक्षा में गुणोत्तर वृद्धि में आधार और गुणक दोनों जाँचें।
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अनुक्रम \(3,13,27,45,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,13,27,45,\ldots\)?
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A \(a_n=2n^2+4n-3\)
B \(a_n=3n\)
C \(a_n=5n^2-2\)
D \(a_n=10n-7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2n^2+4n-3\)
Step 1
Concept
\(2n^2+4n-3\) gives (3,13,27,45). In exams test options with small values of (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2n^2+4n-3\). \(2n^2+4n-3\) gives (3,13,27,45). In exams test options with small values of (n).
Step 3
Exam Tip
\(2n^2+4n-3\) से (3,13,27,45) मिलते हैं। परीक्षा में विकल्पों को छोटे (n) मानों से जाँचें।
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यदि \(a_n=n^2+4n\) है तो पहले तीन पदों का योग क्या होगा?
If \(a_n=n^2+4n\) then what is the sum of the first three terms?
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A (37)
B (38)
C (39)
D (40)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (5,12,21) and the sum is (38). In exams write all terms before adding.
Step 2
Why this answer is correct
The correct answer is B. (38). The first three terms are (5,12,21) and the sum is (38). In exams write all terms before adding.
Step 3
Exam Tip
पहले तीन पद (5,12,21) हैं और योग (38) है। परीक्षा में योग से पहले सभी पद लिखें।
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अनुक्रम \(3,12,21,30,\ldots\) में (111) कौन-सा पद है?
In the sequence \(3,12,21,30,\ldots\) which term is (111)?
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A बारहवाँ पद / (12)th term
B तेरहवाँ पद / (13)th term
C चौदहवाँ पद / (14)th term
D पंद्रहवाँ पद / (15)th term
Explanation opens after your attempt
Correct Answer
B. तेरहवाँ पद / (13)th term
Step 1
Concept
Its rule is \(a_n=9n-6\) and (9n-6=111) gives (n=13). In exams equate the given term to the general term.
Step 2
Why this answer is correct
The correct answer is B. तेरहवाँ पद / (13)th term. Its rule is \(a_n=9n-6\) and (9n-6=111) gives (n=13). In exams equate the given term to the general term.
Step 3
Exam Tip
इसका नियम \(a_n=9n-6\) है और (9n-6=111) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।
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अनुक्रम \(\frac{5}{4},2,\frac{11}{4},\frac{7}{2},\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{5}{4},2,\frac{11}{4},\frac{7}{2},\ldots\)?
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A \(a_n=\frac{n+4}{4}\)
B \(a_n=\frac{3n+2}{4}\)
C \(a_n=\frac{4n+3}{2}\)
D \(a_n=3n-2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{3n+2}{4}\)
Step 1
Concept
\(\frac{3n+2}{4}\) 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. \(a_n=\frac{3n+2}{4}\). \(\frac{3n+2}{4}\) gives the given terms. In exams match fractional terms using small values of (n).
Step 3
Exam Tip
\(\frac{3n+2}{4}\) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को छोटे (n) मानों से मिलाएँ।
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अनुक्रम \(13,24,35,46,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(13,24,35,46,\ldots\)?
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A \(a_n=13n\)
B \(a_n=11n+2\)
C \(a_n=n+12\)
D \(a_n=11n-2\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=11n+2\)
Step 1
Concept
The first term is (13) and the difference is (11) so \(a_n=11n+2\). In exams find the constant part from the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=11n+2\). The first term is (13) and the difference is (11) so \(a_n=11n+2\). In exams find the constant part from the first term.
Step 3
Exam Tip
पहला पद (13) और अंतर (11) है इसलिए \(a_n=11n+2\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।
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अनुक्रम \(3,18,43,78,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(3,18,43,78,\ldots\)?
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A \(a_n=5n^2-2\)
B \(a_n=5n-2\)
C \(a_n=3n^2\)
D \(a_n=15n-12\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n^2-2\)
Step 1
Concept
\(5n^2-2\) gives (3,18,43,78). In exams check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n^2-2\). \(5n^2-2\) gives (3,18,43,78). In exams check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(5n^2-2\) से (3,18,43,78) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम जाँचें।
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अनुक्रम \(4,7,12,21,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,7,12,21,\ldots\)?
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A \(a_n=2^n+n+1\)
B \(a_n=2n+2\)
C \(a_n=n^2+3\)
D \(a_n=3n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2^n+n+1\)
Step 1
Concept
\(2^n+n+1\) gives (4,7,12,21). In exams also check the extra (n) in power-based rules.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2^n+n+1\). \(2^n+n+1\) gives (4,7,12,21). In exams also check the extra (n) in power-based rules.
Step 3
Exam Tip
\(2^n+n+1\) से (4,7,12,21) मिलते हैं। परीक्षा में घात वाले नियमों में अतिरिक्त (n) भी जाँचें।
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यदि \(a_n=n^3+2\) है तो कौन-सा पद (66) के बराबर होगा?
If \(a_n=n^3+2\) then which term is equal to (66)?
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A (n=3)
B (n=4)
C (n=5)
D (n=6)
Explanation opens after your attempt
Step 1
Concept
\(4^3+2=66\) so (n=4). In exams recognize cube numbers.
Step 2
Why this answer is correct
The correct answer is B. (n=4). \(4^3+2=66\) so (n=4). In exams recognize cube numbers.
Step 3
Exam Tip
\(4^3+2=66\) है इसलिए (n=4) है। परीक्षा में घन संख्या पहचानें।
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अनुक्रम \(3,10,29,66,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,10,29,66,\ldots\)?
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A \(a_n=n^2+2\)
B \(a_n=n^3+2\)
C \(a_n=3n\)
D \(a_n=2^n+1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^3+2\)
Step 1
Concept
\(n^3+2\) gives (3,10,29,66). In exams match cube-based rules with the first four terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^3+2\). \(n^3+2\) gives (3,10,29,66). In exams match cube-based rules with the first four terms.
Step 3
Exam Tip
\(n^3+2\) से (3,10,29,66) मिलते हैं। परीक्षा में घन वाले नियम को पहले चार पदों से मिलाएँ।
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अनुक्रम \(2,22,78,188,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,22,78,188,\ldots\)?
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#explicit-rule
#class-9
#medium
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? Hint Small clue
A \(a_n=3n^3-n\)
B \(a_n=2n^3\)
C \(a_n=n^3+1\)
D \(a_n=3n^2-n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^3-n\)
Step 1
Concept
\(3n^3-n\) gives (2,22,78,188). In exams test cube-based options with small (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^3-n\). \(3n^3-n\) gives (2,22,78,188). In exams test cube-based options with small (n).
Step 3
Exam Tip
\(3n^3-n\) से (2,22,78,188) मिलते हैं। परीक्षा में घन आधारित विकल्पों को छोटे (n) से जाँचें।
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अनुक्रम \(88,81,74,67,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(88,81,74,67,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#medium
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A \(a_n=88-7n\)
B \(a_n=95-7n\)
C \(a_n=7n+81\)
D \(a_n=95+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=95-7n\)
Step 1
Concept
At (n=1) it gives (88) and at (n=2) it gives (81) so \(a_n=95-7n\). In exams check the first two terms of a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=95-7n\). At (n=1) it gives (88) and at (n=2) it gives (81) so \(a_n=95-7n\). In exams check the first two terms of a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (88) और (n=2) पर (81) मिलता है इसलिए \(a_n=95-7n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें।
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यदि \(a_n=12n-5\) है तो पहले पाँच पदों का औसत क्या होगा?
If \(a_n=12n-5\) then what is the average of the first five terms?
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#explicit-rule
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A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
The first five terms are (7,19,31,43,55) and the average is (31). In exams divide the sum by the number of terms.
Step 2
Why this answer is correct
The correct answer is A. (31). The first five terms are (7,19,31,43,55) and the average is (31). In exams divide the sum by the number of terms.
Step 3
Exam Tip
पहले पाँच पद (7,19,31,43,55) हैं और औसत (31) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें।
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अनुक्रम \(7,19,31,43,\ldots\) में (151) कौन-सा पद है?
In the sequence \(7,19,31,43,\ldots\) which term is (151)?
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#explicit-rule
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A बारहवाँ पद / (12)th term
B तेरहवाँ पद / (13)th term
C चौदहवाँ पद / (14)th term
D पंद्रहवाँ पद / (15)th term
Explanation opens after your attempt
Correct Answer
B. तेरहवाँ पद / (13)th term
Step 1
Concept
Its rule is \(a_n=12n-5\) and (12n-5=151) gives (n=13). In exams equate the given term to the general term.
Step 2
Why this answer is correct
The correct answer is B. तेरहवाँ पद / (13)th term. Its rule is \(a_n=12n-5\) and (12n-5=151) gives (n=13). In exams equate the given term to the general term.
Step 3
Exam Tip
इसका नियम \(a_n=12n-5\) है और (12n-5=151) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।
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अनुक्रम \(10,18,28,40,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(10,18,28,40,\ldots\)?
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#explicit-rule
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A \(a_n=8n+2\)
B \(a_n=2n^2+4n\)
C \(a_n=n^2+6n+3\)
D \(a_n=n^2+5n+4\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=n^2+5n+4\)
Step 1
Concept
\(n^2+5n+4\) gives (10,18,28,40). In exams test the rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=n^2+5n+4\). \(n^2+5n+4\) gives (10,18,28,40). In exams test the rule on the first four terms.
Step 3
Exam Tip
\(n^2+5n+4\) से (10,18,28,40) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।
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