अनुक्रम \(3,10,21,36,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,10,21,36,\ldots\)?
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A \(a_n=n^2+2n\)
B \(a_n=2n^2+n\)
C \(a_n=3n^2\)
D \(a_n=7n-4\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=2n^2+n\)
Step 1
Concept
\(2n^2+n\) gives (3,10,21,36). In exams, test the rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=2n^2+n\). \(2n^2+n\) gives (3,10,21,36). In exams, test the rule on the first four terms.
Step 3
Exam Tip
\(2n^2+n\) से (3,10,21,36) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।
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यदि \(a_n=3n^2-2n+5\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=3n^2-2n+5\), what is the value of \(a_6\)?
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A (95)
B (99)
C (101)
D (105)
Explanation opens after your attempt
Step 1
Concept
\(a_6=3\times36-12+5=101\). In exams, calculate the square part and linear part separately.
Step 2
Why this answer is correct
The correct answer is C. (101). \(a_6=3\times36-12+5=101\). In exams, calculate the square part and linear part separately.
Step 3
Exam Tip
\(a_6=3\times36-12+5=101\) है। परीक्षा में वर्ग वाला भाग और रैखिक भाग अलग-अलग निकालें।
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अनुक्रम \(5,16,33,56,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(5,16,33,56,\ldots\)?
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A \(a_n=3n^2+2n\)
B \(a_n=5n\)
C \(a_n=2n^2+3\)
D \(a_n=11n-6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+2n\)
Step 1
Concept
Using \(3n^2+2n\) gives the given terms. In exams, substitute (n=1,2,3) to match options.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+2n\). Using \(3n^2+2n\) gives the given terms. In exams, substitute (n=1,2,3) to match options.
Step 3
Exam Tip
\(3n^2+2n\) रखने पर दिए पद मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प मिलाएँ।
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यदि \(a_n=4n^2+n-7\) है, तो \(a_5-a_2\) का मान क्या होगा?
If \(a_n=4n^2+n-7\), what is the value of \(a_5-a_2\)?
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A (81)
B (83)
C (85)
D (87)
Explanation opens after your attempt
Step 1
Concept
\(a_5=98\) and \(a_2=11\), so the difference is (87). In exams, find both terms correctly before subtracting.
Step 2
Why this answer is correct
The correct answer is D. (87). \(a_5=98\) and \(a_2=11\), so the difference is (87). In exams, find both terms correctly before subtracting.
Step 3
Exam Tip
\(a_5=98\) और \(a_2=11\), इसलिए अंतर (87) है। परीक्षा में अंतर निकालने से पहले दोनों पद सही निकालें।
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अनुक्रम \(2,9,22,41,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,9,22,41,\ldots\)?
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A \(a_n=2n^2+1\)
B \(a_n=3n^2-2n+1\)
C \(a_n=n^2+4n-3\)
D \(a_n=7n-5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3n^2-2n+1\)
Step 1
Concept
\(3n^2-2n+1\) gives (2,9,22,41). In exams, use second differences to identify a quadratic rule.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3n^2-2n+1\). \(3n^2-2n+1\) gives (2,9,22,41). In exams, use second differences to identify a quadratic rule.
Step 3
Exam Tip
\(3n^2-2n+1\) से (2,9,22,41) मिलते हैं। परीक्षा में दूसरे अंतर से वर्गीय नियम पहचानें।
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यदि (a_n=\frac{n(n+3)}{2}+2) है, तो \(a_7\) का मान क्या होगा?
If (a_n=\frac{n(n+3)}{2}+2), what is the value of \(a_7\)?
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A (35)
B (37)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
\(a_7=\frac{7\times10}{2}+2=37\). In exams, simplify the fraction first and then add the constant.
Step 2
Why this answer is correct
The correct answer is B. (37). \(a_7=\frac{7\times10}{2}+2=37\). In exams, simplify the fraction first and then add the constant.
Step 3
Exam Tip
\(a_7=\frac{7\times10}{2}+2=37\) है। परीक्षा में पहले भिन्न भाग सरल करें और फिर स्थिर संख्या जोड़ें।
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अनुक्रम \(4,9,16,25,\ldots\) के लिए कौन-सा सामान्य पद सही है?
Which general term is correct for the sequence \(4,9,16,25,\ldots\)?
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A \(a_n=n^2+3\)
B \(a_n=2n^2\)
C (a_n=(n+1)2 )
D \(a_n=4n\)
Explanation opens after your attempt
Correct Answer
C. (a_n=(n+1)2 )
Step 1
Concept
These are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)2 ). In exams, recognize shifted squares.
Step 2
Why this answer is correct
The correct answer is C. (a_n=(n+1)2 ). These are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)2 ). In exams, recognize shifted squares.
Step 3
Exam Tip
ये \(2^2,3^2,4^2,5^2\) हैं, इसलिए (a_n=(n+1)2 ) है। परीक्षा में स्थानांतरित वर्ग पहचानें।
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यदि (a_n=(2n-1)2 ) है, तो \(a_5\) का मान क्या होगा?
If (a_n=(2n-1)2 ), what is the value of \(a_5\)?
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A (49)
B (64)
C (81)
D (100)
Explanation opens after your attempt
Step 1
Concept
(a_5=(10-1)2 =81). In exams, find the bracket value first.
Step 2
Why this answer is correct
The correct answer is C. (81). (a_5=(10-1)2 =81). In exams, find the bracket value first.
Step 3
Exam Tip
(a_5=(10-1)2 =81) है। परीक्षा में कोष्ठक का मान पहले निकालें।
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यदि \(a_n=2n^2+5n-3\) है, तो \(a_4+a_2\) का मान क्या होगा?
If \(a_n=2n^2+5n-3\), what is the value of \(a_4+a_2\)?
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A (51)
B (54)
C (57)
D (60)
Explanation opens after your attempt
Step 1
Concept
\(a_4=49\) and \(a_2=5\), so the sum is (54). In exams, calculate both terms separately before adding.
Step 2
Why this answer is correct
The correct answer is B. (54). \(a_4=49\) and \(a_2=5\), so the sum is (54). In exams, calculate both terms separately before adding.
Step 3
Exam Tip
\(a_4=49\) और \(a_2=5\), इसलिए योग (54) है। परीक्षा में योग से पहले दोनों पद अलग निकालें।
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अनुक्रम \(4,15,34,61,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,15,34,61,\ldots\)?
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A \(a_n=4n^2-n+1\)
B \(a_n=3n^2+1\)
C \(a_n=n^2+10n-7\)
D \(a_n=11n-7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n^2-n+1\)
Step 1
Concept
\(4n^2-n+1\) gives (4,15,34,61). In exams, check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n^2-n+1\). \(4n^2-n+1\) gives (4,15,34,61). In exams, check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(4n^2-n+1\) से (4,15,34,61) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें।
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यदि \(a_n=7n-4\) है, तो \(a_{15}\) का मान क्या होगा?
If \(a_n=7n-4\), what is the value of \(a_{15}\)?
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A (99)
B (101)
C (103)
D (105)
Explanation opens after your attempt
Step 1
Concept
\(a_{15}=7\times15-4=101\). In exams, use direct substitution even for larger (n).
Step 2
Why this answer is correct
The correct answer is B. (101). \(a_{15}=7\times15-4=101\). In exams, use direct substitution even for larger (n).
Step 3
Exam Tip
\(a_{15}=7\times15-4=101\) है। परीक्षा में बड़े (n) के लिए भी सीधे प्रतिस्थापन करें।
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अनुक्रम \(120,112,104,96,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(120,112,104,96,\ldots\)?
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A \(a_n=120-8n\)
B \(a_n=128-8n\)
C \(a_n=8n+112\)
D \(a_n=128+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=128-8n\)
Step 1
Concept
At (n=1) it gives (120), and at (n=2) it gives (112), so \(a_n=128-8n\). In exams, keep the decreasing difference negative.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=128-8n\). At (n=1) it gives (120), and at (n=2) it gives (112), so \(a_n=128-8n\). In exams, keep the decreasing difference negative.
Step 3
Exam Tip
(n=1) पर (120) और (n=2) पर (112) मिलता है, इसलिए \(a_n=128-8n\) है। परीक्षा में घटते अंतर को ऋणात्मक रखें।
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यदि \(a_n=9n+2\) है, तो कौन-सा पद (146) के बराबर होगा?
If \(a_n=9n+2\), which term is equal to (146)?
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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 (9n+2=146), 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 (9n+2=146), we get (n=16). In exams, equate the formula to the given value to find the term number.
Step 3
Exam Tip
(9n+2=146) से (n=16) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(6,15,24,33,\ldots\) में (150) कौन-सा पद है?
In the sequence \(6,15,24,33,\ldots\), which term is (150)?
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A पंद्रहवाँ पद / (15)th term
B सोलहवाँ पद / (16)th term
C सत्रहवाँ पद / (17)th term
D अठारहवाँ पद / (18)th term
Explanation opens after your attempt
Correct Answer
B. सोलहवाँ पद / (16)th term
Step 1
Concept
Its rule is \(a_n=9n-3\), and (9n-3=150) gives (n=17), so the correct term is the (17)th term.
Step 2
Why this answer is correct
The correct answer is B. सोलहवाँ पद / (16)th term. Its rule is \(a_n=9n-3\), and (9n-3=150) gives (n=17), so the correct term is the (17)th term.
Step 3
Exam Tip
इसका नियम \(a_n=9n-3\) है और (9n-3=150) से (n=17) नहीं, (n=17) मिलता है; इसलिए सही पद सत्रहवाँ है।
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अनुक्रम \(2,5,10,17,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,5,10,17,\ldots\)?
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A \(a_n=n^2+1\)
B \(a_n=2n+1\)
C \(a_n=n^2+n\)
D \(a_n=3n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+1\)
Step 1
Concept
\(n^2+1\) gives (2,5,10,17). In exams, also check constant addition to squares.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+1\). \(n^2+1\) gives (2,5,10,17). In exams, also check constant addition to squares.
Step 3
Exam Tip
\(n^2+1\) से (2,5,10,17) मिलते हैं। परीक्षा में वर्ग में स्थिर जोड़ भी जाँचें।
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यदि \(a_n=n^2+1\) है, तो कौन-सा पद (101) के बराबर होगा?
If \(a_n=n^2+1\), which term is equal to (101)?
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A (n=8)
B (n=9)
C (n=10)
D (n=11)
Explanation opens after your attempt
Step 1
Concept
From \(n^2+1=101\), we get \(n^2=100\) and (n=10). In exams, identify perfect squares.
Step 2
Why this answer is correct
The correct answer is C. (n=10). From \(n^2+1=101\), we get \(n^2=100\) and (n=10). In exams, identify perfect squares.
Step 3
Exam Tip
\(n^2+1=101\) से \(n^2=100\) और (n=10) है। परीक्षा में पूर्ण वर्ग पहचानें।
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यदि \(a_n=2^n+3n\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=2^n+3n\), what is the value of \(a_5\)?
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A (45)
B (47)
C (49)
D (51)
Explanation opens after your attempt
Step 1
Concept
\(a_5=32+15=47\). In exams, add both the power and the linear part.
Step 2
Why this answer is correct
The correct answer is B. (47). \(a_5=32+15=47\). In exams, add both the power and the linear part.
Step 3
Exam Tip
\(a_5=32+15=47\) है। परीक्षा में घात और रैखिक भाग दोनों जोड़ें।
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अनुक्रम \(5,10,17,28,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(5,10,17,28,\ldots\)?
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A \(a_n=2^n+3n\)
B \(a_n=n^2+4\)
C \(a_n=5n\)
D \(a_n=2n^2+3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2^n+3n\)
Step 1
Concept
\(2^n+3n\) gives (5,10,17,28). In exams, also check the extra (n)-part in a power rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2^n+3n\). \(2^n+3n\) gives (5,10,17,28). In exams, also check the extra (n)-part in a power rule.
Step 3
Exam Tip
\(2^n+3n\) से (5,10,17,28) मिलते हैं। परीक्षा में घात वाले नियम में अतिरिक्त (n)-वाला भाग भी देखें।
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यदि \(a_n=3^n-2n+1\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=3^n-2n+1\), what is the value of \(a_4\)?
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A (70)
B (72)
C (74)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_4=81-8+1=74\). In exams, find the power and subtract the full linear part.
Step 2
Why this answer is correct
The correct answer is C. (74). \(a_4=81-8+1=74\). In exams, find the power and subtract the full linear part.
Step 3
Exam Tip
\(a_4=81-8+1=74\) है। परीक्षा में घात निकालकर पूरा रैखिक भाग घटाएँ।
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अनुक्रम \(2,6,22,74,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,6,22,74,\ldots\)?
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A \(a_n=3^n-2n+1\)
B \(a_n=3n-1\)
C \(a_n=2^n+n\)
D \(a_n=n^3+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3^n-2n+1\)
Step 1
Concept
\(3^n-2n+1\) gives (2,6,22,74). In exams, check both the power and linear subtraction.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3^n-2n+1\). \(3^n-2n+1\) gives (2,6,22,74). In exams, check both the power and linear subtraction.
Step 3
Exam Tip
\(3^n-2n+1\) से (2,6,22,74) मिलते हैं। परीक्षा में घात और रैखिक घटाव दोनों जाँचें।
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यदि \(a_n=5\cdot2^{n-1}-3\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=5\cdot2^{n-1}-3\), what is the value of \(a_6\)?
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A (153)
B (157)
C (160)
D (163)
Explanation opens after your attempt
Step 1
Concept
\(a_6=5\cdot2^5-3=157\). In exams, pay attention to the exponent (n-1).
Step 2
Why this answer is correct
The correct answer is B. (157). \(a_6=5\cdot2^5-3=157\). In exams, pay attention to the exponent (n-1).
Step 3
Exam Tip
\(a_6=5\cdot2^5-3=157\) है। परीक्षा में (n-1) वाले घातांक पर ध्यान दें।
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अनुक्रम \(2,7,17,37,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(2,7,17,37,\ldots\)?
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#explicit-rule
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A \(a_n=5\cdot2^{n-1}-3\)
B \(a_n=2^n+1\)
C \(a_n=5n-3\)
D \(a_n=3\cdot2^n-4\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5\cdot2^{n-1}-3\)
Step 1
Concept
\(5\cdot2^{n-1}-3\) gives (2,7,17,37). In exams, also check constant subtraction in geometric forms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5\cdot2^{n-1}-3\). \(5\cdot2^{n-1}-3\) gives (2,7,17,37). In exams, also check constant subtraction in geometric forms.
Step 3
Exam Tip
\(5\cdot2^{n-1}-3\) से (2,7,17,37) मिलते हैं। परीक्षा में गुणोत्तर रूप में स्थिर घटाव भी जाँचें।
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यदि \(a_n=3n^2+n-2\) है, तो पहले तीन पदों का योग क्या होगा?
If \(a_n=3n^2+n-2\), what is the sum of the first three terms?
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A (36)
B (38)
C (40)
D (42)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (2,12,26), and the sum is (40). In exams, write all terms before adding.
Step 2
Why this answer is correct
The correct answer is C. (40). The first three terms are (2,12,26), and the sum is (40). In exams, write all terms before adding.
Step 3
Exam Tip
पहले तीन पद (2,12,26) हैं और योग (40) है। परीक्षा में योग से पहले सभी पद लिखें।
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अनुक्रम \(2,12,26,44,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,12,26,44,\ldots\)?
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A \(a_n=3n^2+n-2\)
B \(a_n=2n^2+4\)
C \(a_n=10n-8\)
D \(a_n=n^2+9n-8\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+n-2\)
Step 1
Concept
\(3n^2+n-2\) gives (2,12,26,44). In exams, choose a quadratic rule by checking second differences.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+n-2\). \(3n^2+n-2\) gives (2,12,26,44). In exams, choose a quadratic rule by checking second differences.
Step 3
Exam Tip
\(3n^2+n-2\) से (2,12,26,44) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम चुनें।
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यदि \(a_n=2n^3-n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=2n^3-n\), what is the value of \(a_4\)?
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A (120)
B (122)
C (124)
D (126)
Explanation opens after your attempt
Step 1
Concept
\(a_4=2\times64-4=124\). In exams, handle the cube and linear subtraction separately.
Step 2
Why this answer is correct
The correct answer is C. (124). \(a_4=2\times64-4=124\). In exams, handle the cube and linear subtraction separately.
Step 3
Exam Tip
\(a_4=2\times64-4=124\) है। परीक्षा में घन और रैखिक घटाव अलग-अलग करें।
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अनुक्रम \(1,14,51,124,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(1,14,51,124,\ldots\)?
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A \(a_n=n^3+1\)
B \(a_n=2n^3-n\)
C \(a_n=3n^2-2\)
D \(a_n=13n-12\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=2n^3-n\)
Step 1
Concept
\(2n^3-n\) gives (1,14,51,124). In exams, test cube-based rules with small (n).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=2n^3-n\). \(2n^3-n\) gives (1,14,51,124). In exams, test cube-based rules with small (n).
Step 3
Exam Tip
\(2n^3-n\) से (1,14,51,124) मिलते हैं। परीक्षा में घन आधारित नियमों को छोटे (n) से जाँचें।
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यदि \(a_n=n^3+n^2\) है, तो \(a_5:a_3\) क्या होगा?
If \(a_n=n^3+n^2\), what is \(a_5:a_3\)?
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A (150:36)
B (25:6)
C (6:25)
D (125:27)
Explanation opens after your attempt
Step 1
Concept
\(a_5=150\) and \(a_3=36\), so the simplified ratio is (25:6). In exams, always simplify the ratio.
Step 2
Why this answer is correct
The correct answer is B. (25:6). \(a_5=150\) and \(a_3=36\), so the simplified ratio is (25:6). In exams, always simplify the ratio.
Step 3
Exam Tip
\(a_5=150\) और \(a_3=36\), इसलिए सरल अनुपात (25:6) है। परीक्षा में अनुपात को सरल जरूर करें।
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अनुक्रम \(2,12,36,80,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,12,36,80,\ldots\)?
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A \(a_n=n^3+n^2\)
B \(a_n=2n^3\)
C \(a_n=n^3+1\)
D \(a_n=4n^2-2n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^3+n^2\)
Step 1
Concept
\(n^3+n^2\) gives (2,12,36,80). In exams, check combined cube-and-square rules.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^3+n^2\). \(n^3+n^2\) gives (2,12,36,80). In exams, check combined cube-and-square rules.
Step 3
Exam Tip
\(n^3+n^2\) से (2,12,36,80) मिलते हैं। परीक्षा में घन और वर्ग वाले संयुक्त नियम जाँचें।
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यदि \(a_n=90-6n\) है, तो \(a_3+a_{10}\) का मान क्या होगा?
If \(a_n=90-6n\), what is the value of \(a_3+a_{10}\)?
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A (96)
B (100)
C (102)
D (104)
Explanation opens after your attempt
Step 1
Concept
\(a_3=72\) and \(a_{10}=30\), so the sum is (102). In exams, find both terms carefully in a decreasing formula.
Step 2
Why this answer is correct
The correct answer is C. (102). \(a_3=72\) and \(a_{10}=30\), so the sum is (102). In exams, find both terms carefully in a decreasing formula.
Step 3
Exam Tip
\(a_3=72\) और \(a_{10}=30\), इसलिए योग (102) है। परीक्षा में घटते सूत्र में दोनों पद सावधानी से निकालें।
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अनुक्रम \(84,78,72,66,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(84,78,72,66,\ldots\)?
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A \(a_n=84-6n\)
B \(a_n=90-6n\)
C \(a_n=6n+78\)
D \(a_n=90+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=90-6n\)
Step 1
Concept
At (n=1) it gives (84), and at (n=2) it gives (78), so \(a_n=90-6n\). In exams, check the first two terms of a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=90-6n\). At (n=1) it gives (84), and at (n=2) it gives (78), so \(a_n=90-6n\). In exams, check the first two terms of a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (84) और (n=2) पर (78) मिलता है, इसलिए \(a_n=90-6n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें।
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यदि (a_n=\frac{n(2n+3)}{2}) है, तो \(a_6\) का मान क्या होगा?
If (a_n=\frac{n(2n+3)}{2}), what is the value of \(a_6\)?
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A (41)
B (43)
C (45)
D (47)
Explanation opens after your attempt
Step 1
Concept
\(a_6=\frac{6\times15}{2}=45\). In exams, find the bracket value first and then divide.
Step 2
Why this answer is correct
The correct answer is C. (45). \(a_6=\frac{6\times15}{2}=45\). In exams, find the bracket value first and then divide.
Step 3
Exam Tip
\(a_6=\frac{6\times15}{2}=45\) है। परीक्षा में पहले कोष्ठक का मान निकालें और फिर भाग दें।
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अनुक्रम \(\frac{5}{2},7,\frac{27}{2},22,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(\frac{5}{2},7,\frac{27}{2},22,\ldots\)?
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A (a_n=\frac{n(2n+3)}{2})
B (a_n=\frac{n(n+3)}{2})
C \(a_n=2n+1\)
D \(a_n=\frac{3n^2+1}{2}\)
Explanation opens after your attempt
Correct Answer
A. (a_n=\frac{n(2n+3)}{2})
Step 1
Concept
(\frac{n(2n+3)}{2}) gives the given terms. In exams, test fractional terms using small (n).
Step 2
Why this answer is correct
The correct answer is A. (a_n=\frac{n(2n+3)}{2}). (\frac{n(2n+3)}{2}) gives the given terms. In exams, test fractional terms using small (n).
Step 3
Exam Tip
(\frac{n(2n+3)}{2}) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी छोटे (n) से जाँचें।
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यदि \(a_n=4^n-n^2\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=4^n-n^2\), what is the value of \(a_3\)?
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A (51)
B (53)
C (55)
D (57)
Explanation opens after your attempt
Step 1
Concept
\(a_3=64-9=55\). In exams, calculate both the power and the square correctly.
Step 2
Why this answer is correct
The correct answer is C. (55). \(a_3=64-9=55\). In exams, calculate both the power and the square correctly.
Step 3
Exam Tip
\(a_3=64-9=55\) है। परीक्षा में घात और वर्ग दोनों सही निकालें।
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अनुक्रम \(3,12,55,240,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,12,55,240,\ldots\)?
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A \(a_n=4^n-n^2\)
B \(a_n=4n^2-1\)
C \(a_n=2^n+n\)
D \(a_n=n^4-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4^n-n^2\)
Step 1
Concept
\(4^n-n^2\) gives (3,12,55,240). In exams, also check rules where a square is subtracted from a power.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4^n-n^2\). \(4^n-n^2\) gives (3,12,55,240). In exams, also check rules where a square is subtracted from a power.
Step 3
Exam Tip
\(4^n-n^2\) से (3,12,55,240) मिलते हैं। परीक्षा में घात में से वर्ग घटाने वाले नियम भी जाँचें।
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यदि \(a_n=12n-7\) है, तो पहले पाँच पदों का औसत क्या होगा?
If \(a_n=12n-7\), what is the average of the first five terms?
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A (29)
B (31)
C (33)
D (35)
Explanation opens after your attempt
Step 1
Concept
The first five terms are (5,17,29,41,53), and the average is (29). In exams, divide the sum by the number of terms.
Step 2
Why this answer is correct
The correct answer is A. (29). The first five terms are (5,17,29,41,53), and the average is (29). In exams, divide the sum by the number of terms.
Step 3
Exam Tip
पहले पाँच पद (5,17,29,41,53) हैं और औसत (29) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें।
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अनुक्रम \(5,17,29,41,\ldots\) में (149) कौन-सा पद है?
In the sequence \(5,17,29,41,\ldots\), which term is (149)?
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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 \(a_n=12n-7\), and (12n-7=149) 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 \(a_n=12n-7\), and (12n-7=149) gives (n=13). In exams, equate the given term to the general term.
Step 3
Exam Tip
इसका नियम \(a_n=12n-7\) है और (12n-7=149) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।
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यदि \(a_n=6n^2-4n+3\) है, तो कौन-सा कथन सही है?
If \(a_n=6n^2-4n+3\), which statement is correct?
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A \(a_2=19\) और \(a_3=45\) / \(a_2=19\) and \(a_3=45\)
B \(a_2=18\) और \(a_3=45\) / \(a_2=18\) and \(a_3=45\)
C \(a_2=19\) और \(a_3=44\) / \(a_2=19\) and \(a_3=44\)
D \(a_2=20\) और \(a_3=46\) / \(a_2=20\) and \(a_3=46\)
Explanation opens after your attempt
Correct Answer
A. \(a_2=19\) और \(a_3=45\) / \(a_2=19\) and \(a_3=45\)
Step 1
Concept
\(a_2=24-8+3=19\) and \(a_3=54-12+3=45\). In exams, use a new value of (n) for each term.
Step 2
Why this answer is correct
The correct answer is A. \(a_2=19\) और \(a_3=45\) / \(a_2=19\) and \(a_3=45\). \(a_2=24-8+3=19\) and \(a_3=54-12+3=45\). In exams, use a new value of (n) for each term.
Step 3
Exam Tip
\(a_2=24-8+3=19\) और \(a_3=54-12+3=45\) है। परीक्षा में हर पद के लिए (n) का नया मान रखें।
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अनुक्रम \(5,19,45,83,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(5,19,45,83,\ldots\)?
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A \(a_n=6n^2-4n+3\)
B \(a_n=5n\)
C \(a_n=7n^2-2\)
D \(a_n=14n-9\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n^2-4n+3\)
Step 1
Concept
\(6n^2-4n+3\) gives (5,19,45,83). In exams, choose a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n^2-4n+3\). \(6n^2-4n+3\) gives (5,19,45,83). In exams, choose a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(6n^2-4n+3\) से (5,19,45,83) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम चुनें।
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यदि \(a_n=5^n-2n\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=5^n-2n\), what is the value of \(a_3\)?
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A (117)
B (119)
C (121)
D (123)
Explanation opens after your attempt
Step 1
Concept
\(a_3=125-6=119\). In exams, find the power and subtract (2n).
Step 2
Why this answer is correct
The correct answer is B. (119). \(a_3=125-6=119\). In exams, find the power and subtract (2n).
Step 3
Exam Tip
\(a_3=125-6=119\) है। परीक्षा में घात निकालकर (2n) घटाएँ।
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अनुक्रम \(3,21,119,617,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,21,119,617,\ldots\)?
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A \(a_n=5^n-2n\)
B \(a_n=5n-2\)
C \(a_n=2^n+1\)
D \(a_n=n^5-2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5^n-2n\)
Step 1
Concept
\(5^n-2n\) gives (3,21,119,617). In exams, also check subtraction of a linear term from a power.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5^n-2n\). \(5^n-2n\) gives (3,21,119,617). In exams, also check subtraction of a linear term from a power.
Step 3
Exam Tip
\(5^n-2n\) से (3,21,119,617) मिलते हैं। परीक्षा में घात में से रैखिक पद घटाकर भी जाँचें।
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यदि \(a_n=2n^2+7n-4\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=2n^2+7n-4\), what is the value of \(a_6\)?
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A (106)
B (108)
C (110)
D (112)
Explanation opens after your attempt
Step 1
Concept
\(a_6=72+42-4=110\). In exams, write positive and negative terms separately.
Step 2
Why this answer is correct
The correct answer is C. (110). \(a_6=72+42-4=110\). In exams, write positive and negative terms separately.
Step 3
Exam Tip
\(a_6=72+42-4=110\) है। परीक्षा में धन और ऋण पदों को अलग-अलग लिखें।
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अनुक्रम \(5,18,35,56,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(5,18,35,56,\ldots\)?
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#progressions
#explicit-rule
#class-9
#expert
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A \(a_n=2n^2+7n-4\)
B \(a_n=5n\)
C \(a_n=13n-8\)
D \(a_n=n^2+12n-8\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2n^2+7n-4\)
Step 1
Concept
\(2n^2+7n-4\) gives (5,18,35,56). In exams, test the quadratic rule with small (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2n^2+7n-4\). \(2n^2+7n-4\) gives (5,18,35,56). In exams, test the quadratic rule with small (n).
Step 3
Exam Tip
\(2n^2+7n-4\) से (5,18,35,56) मिलते हैं। परीक्षा में वर्गीय नियम को छोटे (n) से जाँचें।
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यदि \(a_n=\frac{2n^2+5n}{3}\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=\frac{2n^2+5n}{3}\), what is the value of \(a_6\)?
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#explicit-rule
#class-9
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A (32)
B (34)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
\(a_6=\frac{72+30}{3}=34\). In exams, simplify the whole numerator and then divide by the denominator.
Step 2
Why this answer is correct
The correct answer is B. (34). \(a_6=\frac{72+30}{3}=34\). In exams, simplify the whole numerator and then divide by the denominator.
Step 3
Exam Tip
\(a_6=\frac{72+30}{3}=34\) है। परीक्षा में अंश पूरा सरल करके हर से भाग दें।
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अनुक्रम \(\frac{7}{3},6,11,\frac{52}{3},\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{7}{3},6,11,\frac{52}{3},\ldots\)?
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#explicit-rule
#class-9
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A \(a_n=\frac{2n^2+5n}{3}\)
B (a_n=\frac{n(n+1)}{2})
C \(a_n=2n+1\)
D \(a_n=\frac{3n^2+1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{2n^2+5n}{3}\)
Step 1
Concept
\(\frac{2n^2+5n}{3}\) gives the given terms. In exams, match fractional terms with options too.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{2n^2+5n}{3}\). \(\frac{2n^2+5n}{3}\) gives the given terms. In exams, match fractional terms with options too.
Step 3
Exam Tip
\(\frac{2n^2+5n}{3}\) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी विकल्पों से मिलाएँ।
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यदि \(a_n=4n^2+3n+2\) है, तो \(a_4-a_1\) का मान क्या होगा?
If \(a_n=4n^2+3n+2\), what is the value of \(a_4-a_1\)?
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A (66)
B (69)
C (72)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(a_4=78\) and \(a_1=9\), so the difference is (69). In exams, check both values before the final subtraction.
Step 2
Why this answer is correct
The correct answer is B. (69). \(a_4=78\) and \(a_1=9\), so the difference is (69). In exams, check both values before the final subtraction.
Step 3
Exam Tip
\(a_4=78\) और \(a_1=9\), इसलिए अंतर (69) है। परीक्षा में अंतिम घटाव से पहले दोनों मान जाँचें।
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अनुक्रम \(9,24,47,78,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(9,24,47,78,\ldots\)?
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A \(a_n=4n^2+3n+2\)
B \(a_n=9n\)
C \(a_n=5n^2+4\)
D \(a_n=15n-6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n^2+3n+2\)
Step 1
Concept
\(4n^2+3n+2\) gives (9,24,47,78). In exams, check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n^2+3n+2\). \(4n^2+3n+2\) gives (9,24,47,78). In exams, check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(4n^2+3n+2\) से (9,24,47,78) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें।
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यदि \(a_n=3\cdot2^n-n\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=3\cdot2^n-n\), what is the value of \(a_5\)?
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A (89)
B (91)
C (93)
D (95)
Explanation opens after your attempt
Step 1
Concept
\(a_5=3\cdot32-5=91\). In exams, subtract the current (n) after finding the power.
Step 2
Why this answer is correct
The correct answer is B. (91). \(a_5=3\cdot32-5=91\). In exams, subtract the current (n) after finding the power.
Step 3
Exam Tip
\(a_5=3\cdot32-5=91\) है। परीक्षा में घात के बाद वर्तमान (n) घटाएँ।
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अनुक्रम \(5,10,21,44,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(5,10,21,44,\ldots\)?
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A \(a_n=3\cdot2^n-n\)
B \(a_n=5n\)
C \(a_n=2^n+n\)
D \(a_n=n^2+4\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3\cdot2^n-n\)
Step 1
Concept
\(3\cdot2^n-n\) gives (5,10,21,44). In exams, check both the power and the subtracted (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3\cdot2^n-n\). \(3\cdot2^n-n\) gives (5,10,21,44). In exams, check both the power and the subtracted (n).
Step 3
Exam Tip
\(3\cdot2^n-n\) से (5,10,21,44) मिलते हैं। परीक्षा में घात और घटते (n) दोनों देखें।
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यदि \(a_n=5n^2-6n+4\) है, तो \(a_5+a_2\) का मान क्या होगा?
If \(a_n=5n^2-6n+4\), what is the value of \(a_5+a_2\)?
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A (107)
B (109)
C (111)
D (113)
Explanation opens after your attempt
Step 1
Concept
\(a_5=99\) and \(a_2=8\), so the sum is (107). In exams, handle signs carefully in a quadratic formula.
Step 2
Why this answer is correct
The correct answer is A. (107). \(a_5=99\) and \(a_2=8\), so the sum is (107). In exams, handle signs carefully in a quadratic formula.
Step 3
Exam Tip
\(a_5=99\) और \(a_2=8\), इसलिए योग (107) है। परीक्षा में वर्गीय सूत्र में चिह्न सावधानी से रखें।
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अनुक्रम \(6,20,42,72,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(6,20,42,72,\ldots\)?
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A \(a_n=6n\)
B \(a_n=2n^2+4n\)
C \(a_n=4n^2-2n\)
D \(a_n=4n^2+2n\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=4n^2+2n\)
Step 1
Concept
\(4n^2+2n\) gives (6,20,42,72). In exams, test the rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=4n^2+2n\). \(4n^2+2n\) gives (6,20,42,72). In exams, test the rule on the first four terms.
Step 3
Exam Tip
\(4n^2+2n\) से (6,20,42,72) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।
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