अनुक्रम \(18,14,10,6,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(18,14,10,6,\ldots\)?
#sequences
#progressions
#decreasing-sequence
#general-rule
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A \(a_n=18-4n\)
B \(a_n=22+4n\)
C \(a_n=4n+14\)
D \(a_n=22-4n\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=22-4n\)
Step 1
Concept
The first term is (18) and the difference is (-4), so (a_n=18+(n-1)(-4)=22-4n). Keep the difference negative in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=22-4n\). The first term is (18) and the difference is (-4), so (a_n=18+(n-1)(-4)=22-4n). Keep the difference negative in a decreasing sequence.
Step 3
Exam Tip
पहला पद (18) और अंतर (-4) है इसलिए (a_n=18+(n-1)(-4)=22-4n)। घटते अनुक्रम में अंतर को ऋणात्मक रखें।
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यदि \(a_n=4n^2-3n\) है तो \(a_5\) का मान क्या होगा?
If \(a_n=4n^2-3n\), what is the value of \(a_5\)?
#sequences
#progressions
#explicit-rule
#nth-term
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A (85)
B (90)
C (95)
D (100)
Explanation opens after your attempt
Step 1
Concept
(a_5=4(5)2 -3(5)=100-15=85). Substitute the correct term number for (n) while finding a term.
Step 2
Why this answer is correct
The correct answer is A. (85). (a_5=4(5)2 -3(5)=100-15=85). Substitute the correct term number for (n) while finding a term.
Step 3
Exam Tip
(a_5=4(5)2 -3(5)=100-15=85)। पद निकालते समय (n) की जगह सही पद-संख्या रखें।
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यदि \(a_n=6n+1\) है तो \(a_n=55\) किस पद पर होगा?
If \(a_n=6n+1\), at which term will \(a_n=55\)?
#sequences
#progressions
#term-position
#linear-rule
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
C. (9)वाँ / (9)th
Step 1
Concept
From (6n+1=55), (6n=54) and (n=9). When position is asked, set the rule equal to the given term.
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. From (6n+1=55), (6n=54) and (n=9). When position is asked, set the rule equal to the given term.
Step 3
Exam Tip
(6n+1=55) से (6n=54) और (n=9)। पद का स्थान पूछे तो नियम को दिए पद के बराबर रखें।
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यदि \(a_n=n^2+3n+2\) है तो पहले चार पद कौन-से हैं?
If \(a_n=n^2+3n+2\), what are the first four terms?
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#progressions
#quadratic-sequence
#explicit-rule
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A (4,10,18,28)
B (5,12,21,32)
C (6,14,24,36)
D (6,12,20,30)
Explanation opens after your attempt
Correct Answer
D. (6,12,20,30)
Step 1
Concept
Putting (n=1,2,3,4) gives (6,12,20,30). Start (n) from (1) when forming terms from a rule.
Step 2
Why this answer is correct
The correct answer is D. (6,12,20,30). Putting (n=1,2,3,4) gives (6,12,20,30). Start (n) from (1) when forming terms from a rule.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (6,12,20,30) मिलते हैं। नियम से पद निकालते समय (n) को (1) से शुरू करें।
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अनुक्रम \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\frac{5}{9},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\frac{5}{9},\ldots\)?
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#progressions
#fraction-sequence
#general-rule
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A \(a_n=\frac{n+1}{2n+1}\)
B \(a_n=\frac{n}{2n+1}\)
C \(a_n=\frac{n+1}{2n-1}\)
D \(a_n=\frac{2n}{n+1}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{n+1}{2n+1}\)
Step 1
Concept
The numerator is (n+1) and the denominator is (2n+1), so \(a_n=\frac{n+1}{2n+1}\). In fractions observe numerator and denominator patterns separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{n+1}{2n+1}\). The numerator is (n+1) and the denominator is (2n+1), so \(a_n=\frac{n+1}{2n+1}\). In fractions observe numerator and denominator patterns separately.
Step 3
Exam Tip
अंश (n+1) और हर (2n+1) है इसलिए \(a_n=\frac{n+1}{2n+1}\)। भिन्न में अंश और हर के पैटर्न अलग देखें।
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किस विकल्प से (a_n=n(n+2)) के पहले चार पद मिलते हैं?
Which option gives the first four terms of (a_n=n(n+2))?
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#progressions
#product-pattern
#explicit-rule
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A (2,6,12,20)
B (4,8,14,22)
C (3,8,15,24)
D (5,10,17,26)
Explanation opens after your attempt
Correct Answer
C. (3,8,15,24)
Step 1
Concept
Putting (n=1,2,3,4) gives (3,8,15,24). In a product-form rule direct substitution is easy.
Step 2
Why this answer is correct
The correct answer is C. (3,8,15,24). Putting (n=1,2,3,4) gives (3,8,15,24). In a product-form rule direct substitution is easy.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (3,8,15,24) मिलते हैं। गुणन रूप वाले नियम में सीधे मान रखना आसान है।
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यदि अनुक्रम का नियम \(a_n=5\cdot2^{n-1}\) है तो पाँचवाँ पद क्या होगा?
If the rule of a sequence is \(a_n=5\cdot2^{n-1}\), what is the fifth term?
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#geometric-sequence
#explicit-rule
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A (40)
B (80)
C (160)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_5=5\cdot2^4=80\). In an exponential rule find the value of (n-1) first.
Step 2
Why this answer is correct
The correct answer is B. (80). \(a_5=5\cdot2^4=80\). In an exponential rule find the value of (n-1) first.
Step 3
Exam Tip
\(a_5=5\cdot2^4=80\)। घात वाले नियम में (n-1) का मान पहले निकालें।
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अनुक्रम \(1,-2,3,-4,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,-2,3,-4,\ldots\)?
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#alternating-sequence
#general-rule
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A (a_n=(-1)^{n+1}n)
B (a_n=(-1)^n n)
C \(a_n=n+1\)
D (a_n=(-1)^{n+1}(n+1))
Explanation opens after your attempt
Correct Answer
A. (a_n=(-1)^{n+1}n)
Step 1
Concept
The sign alternates and the magnitude is (n), so (a_n=(-1)^{n+1}n). In alternating signs choose the power of ((-1)^n) carefully.
Step 2
Why this answer is correct
The correct answer is A. (a_n=(-1)^{n+1}n). The sign alternates and the magnitude is (n), so (a_n=(-1)^{n+1}n). In alternating signs choose the power of ((-1)^n) carefully.
Step 3
Exam Tip
चिह्न बारी-बारी से बदलता है और परिमाण (n) है इसलिए (a_n=(-1)^{n+1}n)। वैकल्पिक चिह्न में ((-1)^n) की शक्ति ध्यान से चुनें।
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अनुक्रम \(1,8,27,64,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(1,8,27,64,\ldots\)?
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#cube-sequence
#general-rule
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A \(a_n=n^2\)
B \(a_n=2^n\)
C \(a_n=n^3\)
D (a_n=(n+1)3 )
Explanation opens after your attempt
Correct Answer
C. \(a_n=n^3\)
Step 1
Concept
This is \(1^3,2^3,3^3,4^3,\ldots\), so \(a_n=n^3\). In cube sequences identify terms as cubes.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=n^3\). This is \(1^3,2^3,3^3,4^3,\ldots\), so \(a_n=n^3\). In cube sequences identify terms as cubes.
Step 3
Exam Tip
यह \(1^3,2^3,3^3,4^3,\ldots\) है इसलिए \(a_n=n^3\)। घन अनुक्रम में पदों को घन रूप में पहचानें।
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अनुक्रम \(5,11,19,29,\ldots\) का (8)वाँ पद क्या होगा?
What will be the (8)th term of the sequence \(5,11,19,29,\ldots\)?
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#quadratic-sequence
#nth-term
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A (77)
B (81)
C (85)
D (89)
Explanation opens after your attempt
Step 1
Concept
Its rule is \(a_n=n^2+3n+1\), so \(a_8=64+24+1=89\). First identify the general rule and then find the term.
Step 2
Why this answer is correct
The correct answer is D. (89). Its rule is \(a_n=n^2+3n+1\), so \(a_8=64+24+1=89\). First identify the general rule and then find the term.
Step 3
Exam Tip
इसका नियम \(a_n=n^2+3n+1\) है इसलिए \(a_8=64+24+1=89\)। पहले सामान्य नियम पहचानें फिर पद निकालें।
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अनुक्रम \(8,12,16,20,\ldots\) में (50) के बारे में सही कथन कौन-सा है?
Which statement about (50) is correct for the sequence \(8,12,16,20,\ldots\)?
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#progressions
#term-checking
#arithmetic-sequence
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A (50) पाँचवाँ पद है / (50) is the fifth term
B (50) आठवाँ पद है / (50) is the eighth term
C (50) इस अनुक्रम का पद नहीं है / (50) is not a term of this sequence
D (50) ग्यारहवाँ पद है / (50) is the eleventh term
Explanation opens after your attempt
Correct Answer
C. (50) इस अनुक्रम का पद नहीं है / (50) is not a term of this sequence
Step 1
Concept
The general term is \(a_n=4n+4\), and (4n+4=50) gives \(n=\frac{23}{2}\). If the position is not a natural number, the given number is not a term.
Step 2
Why this answer is correct
The correct answer is C. (50) इस अनुक्रम का पद नहीं है / (50) is not a term of this sequence. The general term is \(a_n=4n+4\), and (4n+4=50) gives \(n=\frac{23}{2}\). If the position is not a natural number, the given number is not a term.
Step 3
Exam Tip
सामान्य पद \(a_n=4n+4\) है और (4n+4=50) से \(n=\frac{23}{2}\) मिलता है। पद-संख्या प्राकृतिक संख्या न हो तो दिया पद अनुक्रम में नहीं होगा।
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अनुक्रम \(1,9,25,49,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,9,25,49,\ldots\)?
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#progressions
#odd-squares
#general-rule
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A (a_n=(2n)2 )
B (a_n=(2n-1)2 )
C \(a_n=n^2+1\)
D \(a_n=2n^2-1\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(2n-1)2 )
Step 1
Concept
These are squares of odd numbers \(1^2,3^2,5^2,7^2,\ldots\), so (a_n=(2n-1)2 ). In squares observe the base pattern.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(2n-1)2 ). These are squares of odd numbers \(1^2,3^2,5^2,7^2,\ldots\), so (a_n=(2n-1)2 ). In squares observe the base pattern.
Step 3
Exam Tip
यह विषम संख्याओं के वर्ग \(1^2,3^2,5^2,7^2,\ldots\) हैं इसलिए (a_n=(2n-1)2 )। वर्गों में आधार का पैटर्न देखें।
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यदि \(a_n=5^n\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=5^n\), what is the value of \(a_4\)?
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#progressions
#exponential-sequence
#nth-term
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A (125)
B (250)
C (500)
D (625)
Explanation opens after your attempt
Step 1
Concept
\(a_4=5^4=625\). In exponential rules remember repeated multiplication.
Step 2
Why this answer is correct
The correct answer is D. (625). \(a_4=5^4=625\). In exponential rules remember repeated multiplication.
Step 3
Exam Tip
\(a_4=5^4=625\)। घातांक वाले नियम में गुणा बार-बार करना याद रखें।
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अनुक्रम \(\frac{1}{2},\frac{3}{3},\frac{5}{4},\frac{7}{5},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{1}{2},\frac{3}{3},\frac{5}{4},\frac{7}{5},\ldots\)?
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#progressions
#fraction-sequence
#general-rule
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A \(a_n=\frac{2n-1}{n+1}\)
B \(a_n=\frac{n}{2n-1}\)
C \(a_n=\frac{2n+1}{n}\)
D \(a_n=\frac{n+1}{2n-1}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{2n-1}{n+1}\)
Step 1
Concept
The numerator is (2n-1) and the denominator is (n+1), so \(a_n=\frac{2n-1}{n+1}\). In a fraction sequence form rules for both parts separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{2n-1}{n+1}\). The numerator is (2n-1) and the denominator is (n+1), so \(a_n=\frac{2n-1}{n+1}\). In a fraction sequence form rules for both parts separately.
Step 3
Exam Tip
अंश (2n-1) और हर (n+1) है इसलिए \(a_n=\frac{2n-1}{n+1}\)। भिन्न अनुक्रम में दोनों भागों का अलग नियम बनाएं।
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एक समानांतर अनुक्रम में \(a_2=7\) और \(a_5=16\) है। उसका सामान्य पद क्या है?
In an arithmetic sequence, \(a_2=7\) and \(a_5=16\). What is its general term?
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#arithmetic-sequence
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A \(a_n=2n+3\)
B \(a_n=4n-1\)
C \(a_n=3n+1\)
D \(a_n=5n-3\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=3n+1\)
Step 1
Concept
\(a_5-a_2=9\) and there are three gaps, so (d=3), then \(a_n=3n+1\). From two given terms first find the common difference.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=3n+1\). \(a_5-a_2=9\) and there are three gaps, so (d=3), then \(a_n=3n+1\). From two given terms first find the common difference.
Step 3
Exam Tip
\(a_5-a_2=9\) और तीन अंतर हैं इसलिए (d=3), फिर \(a_n=3n+1\)। दो दिए पदों से पहले समान अंतर निकालें।
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किस विकल्प में \(a_n=n^2+3n-1\) से बने पहले तीन पद हैं?
Which option contains the first three terms formed by \(a_n=n^2+3n-1\)?
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#sequence-from-rule
#quadratic-rule
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A (2,9,18)
B (3,9,17)
C (4,10,18)
D (5,11,19)
Explanation opens after your attempt
Correct Answer
B. (3,9,17)
Step 1
Concept
Putting (n=1,2,3) gives (3,9,17). To check options, quickly find the initial terms.
Step 2
Why this answer is correct
The correct answer is B. (3,9,17). Putting (n=1,2,3) gives (3,9,17). To check options, quickly find the initial terms.
Step 3
Exam Tip
(n=1,2,3) रखने पर (3,9,17) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद जल्दी निकालें।
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यदि \(a_1=4\) और प्रत्येक अगला पद पिछले पद से (6) अधिक है, तो स्पष्ट नियम क्या होगा?
If \(a_1=4\) and each next term is (6) more than the previous term, what is the explicit rule?
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#word-problem
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A \(a_n=6n-2\)
B \(a_n=4n+6\)
C \(a_n=6n+4\)
D \(a_n=4n-2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n-2\)
Step 1
Concept
The first term is (4) and the difference is (6), so (a_n=4+(n-1)6=6n-2). Do not forget the first term while forming a rule from words.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n-2\). The first term is (4) and the difference is (6), so (a_n=4+(n-1)6=6n-2). Do not forget the first term while forming a rule from words.
Step 3
Exam Tip
पहला पद (4) और अंतर (6) है इसलिए (a_n=4+(n-1)6=6n-2)। वर्णन से नियम बनाते समय पहला पद न भूलें।
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यदि \(a_n=\frac{n}{n+2}\) है तो \(a_n=\frac{5}{7}\) किस पद पर होगा?
If \(a_n=\frac{n}{n+2}\), at which term will \(a_n=\frac{5}{7}\)?
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#progressions
#fraction-sequence
#term-position
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A (3)वाँ / (3)rd
B (4)वाँ / (4)th
C (6)वाँ / (6)th
D (5)वाँ / (5)th
Explanation opens after your attempt
Correct Answer
D. (5)वाँ / (5)th
Step 1
Concept
From \(\frac{n}{n+2}=\frac{5}{7}\), (7n=5n+10) and (n=5). Use cross multiplication in fractional equations.
Step 2
Why this answer is correct
The correct answer is D. (5)वाँ / (5)th. From \(\frac{n}{n+2}=\frac{5}{7}\), (7n=5n+10) and (n=5). Use cross multiplication in fractional equations.
Step 3
Exam Tip
\(\frac{n}{n+2}=\frac{5}{7}\) से (7n=5n+10) और (n=5)। भिन्न समीकरण में क्रॉस गुणा करें।
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यदि \(a_n=2n^2+3\) है तो \(a_3+a_4\) का मान क्या है?
If \(a_n=2n^2+3\), what is the value of \(a_3+a_4\)?
#sequences
#progressions
#sum-of-terms
#explicit-rule
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A (56)
B (52)
C (60)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(a_3=21\) and \(a_4=35\), so the sum is (56). Find both terms separately before adding.
Step 2
Why this answer is correct
The correct answer is A. (56). \(a_3=21\) and \(a_4=35\), so the sum is (56). Find both terms separately before adding.
Step 3
Exam Tip
\(a_3=21\) और \(a_4=35\), इसलिए योग (56) है। जोड़ने से पहले दोनों पद अलग-अलग निकालें।
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यदि \(a_n=2^n+n\) है तो पहले चार पद कौन-से होंगे?
If \(a_n=2^n+n\), what will be the first four terms?
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#progressions
#exponential-sequence
#explicit-rule
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A (2,5,10,17)
B (4,7,12,19)
C (3,7,12,20)
D (3,6,11,20)
Explanation opens after your attempt
Correct Answer
D. (3,6,11,20)
Step 1
Concept
Putting (n=1,2,3,4) gives (3,6,11,20). Add both the power part and (n) together.
Step 2
Why this answer is correct
The correct answer is D. (3,6,11,20). Putting (n=1,2,3,4) gives (3,6,11,20). Add both the power part and (n) together.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (3,6,11,20) मिलते हैं। घात और (n) दोनों को साथ जोड़ें।
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अनुक्रम \(-3,5,-7,9,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(-3,5,-7,9,\ldots\)?
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#progressions
#alternating-sequence
#general-rule
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A (a_n=(-1)^n(2n+1))
B (a_n=(-1)^{n+1}(2n+1))
C \(a_n=2n+1\)
D (a_n=(-1)^n n)
Explanation opens after your attempt
Correct Answer
A. (a_n=(-1)^n(2n+1))
Step 1
Concept
The magnitude is \(3,5,7,9,\ldots\) and the signs start negative and alternate, so (a_n=(-1)^n(2n+1)). In alternating signs always check the sign of the first term.
Step 2
Why this answer is correct
The correct answer is A. (a_n=(-1)^n(2n+1)). The magnitude is \(3,5,7,9,\ldots\) and the signs start negative and alternate, so (a_n=(-1)^n(2n+1)). In alternating signs always check the sign of the first term.
Step 3
Exam Tip
परिमाण \(3,5,7,9,\ldots\) है और चिह्न ऋण से शुरू होकर बदलता है, इसलिए (a_n=(-1)^n(2n+1))। वैकल्पिक चिह्न में पहले पद का चिह्न जरूर जांचें।
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अनुक्रम \(7,13,19,25,\ldots\) का (25)वाँ पद क्या है?
What is the (25)th term of the sequence \(7,13,19,25,\ldots\)?
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A (139)
B (145)
C (151)
D (157)
Explanation opens after your attempt
Step 1
Concept
The general term is \(a_n=6n+1\), so \(a_{25}=151\). Use the same general rule even for a large term.
Step 2
Why this answer is correct
The correct answer is C. (151). The general term is \(a_n=6n+1\), so \(a_{25}=151\). Use the same general rule even for a large term.
Step 3
Exam Tip
सामान्य पद \(a_n=6n+1\) है इसलिए \(a_{25}=151\)। बड़े पद के लिए भी वही सामान्य नियम लगाएं।
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यदि \(a_n=n^2+2n\) है तो \(a_n=80\) किस (n) पर होगा?
If \(a_n=n^2+2n\), for which (n) will \(a_n=80\)?
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A (6)
B (7)
C (9)
D (8)
Explanation opens after your attempt
Step 1
Concept
Putting (n=8) in \(n^2+2n=80\) gives (64+16=80). Directly checking options is a quick method.
Step 2
Why this answer is correct
The correct answer is D. (8). Putting (n=8) in \(n^2+2n=80\) gives (64+16=80). Directly checking options is a quick method.
Step 3
Exam Tip
\(n^2+2n=80\) में (n=8) रखने पर (64+16=80) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।
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अनुक्रम \(1,2,5,10,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,2,5,10,\ldots\)?
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#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2-2n+2\)
B \(a_n=n^2+1\)
C \(a_n=n^2-n\)
D \(a_n=2n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-2n+2\)
Step 1
Concept
\(n^2-2n+2\) gives (1,2,5,10). In a sequence with increasing differences, check quadratic options.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-2n+2\). \(n^2-2n+2\) gives (1,2,5,10). In a sequence with increasing differences, check quadratic options.
Step 3
Exam Tip
\(n^2-2n+2\) से (1,2,5,10) मिलते हैं। बढ़ते अंतर वाले क्रम में द्विघात विकल्प जांचें।
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यदि \(a_n=\frac{2n+3}{n+1}\) है तो \(a_4\) क्या होगा?
If \(a_n=\frac{2n+3}{n+1}\), what is \(a_4\)?
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#progressions
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A \(\frac{9}{5}\)
B \(\frac{10}{5}\)
C \(\frac{11}{5}\)
D \(\frac{12}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{11}{5}\)
Step 1
Concept
(a_4=\frac{2(4)+3}{4+1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{11}{5}\). (a_4=\frac{2(4)+3}{4+1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
Step 3
Exam Tip
(a_4=\frac{2(4)+3}{4+1}=\frac{11}{5})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें।
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अनुक्रम \(8,27,64,125,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(8,27,64,125,\ldots\)?
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#progressions
#cube-sequence
#general-rule
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A \(a_n=n^3\)
B (a_n=(n+1)3 )
C \(a_n=n^3+1\)
D (a_n=(n+2)3 )
Explanation opens after your attempt
Correct Answer
B. (a_n=(n+1)3 )
Step 1
Concept
This is \(2^3,3^3,4^3,5^3,\ldots\), so (a_n=(n+1)3 ). In cube sequences identify the base number.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(n+1)3 ). This is \(2^3,3^3,4^3,5^3,\ldots\), so (a_n=(n+1)3 ). In cube sequences identify the base number.
Step 3
Exam Tip
यह \(2^3,3^3,4^3,5^3,\ldots\) है इसलिए (a_n=(n+1)3 )। घन अनुक्रम में आधार संख्या पहचानें।
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यदि \(a_n=4n^2-1\) है तो \(a_5+a_1\) का मान क्या होगा?
If \(a_n=4n^2-1\), what is the value of \(a_5+a_1\)?
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#quadratic-rule
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A (96)
B (100)
C (102)
D (104)
Explanation opens after your attempt
Step 1
Concept
\(a_5=99\) and \(a_1=3\), so the sum is (102). Find both terms before adding.
Step 2
Why this answer is correct
The correct answer is C. (102). \(a_5=99\) and \(a_1=3\), so the sum is (102). Find both terms before adding.
Step 3
Exam Tip
\(a_5=99\) और \(a_1=3\), इसलिए योग (102) है। दोनों पद निकालकर ही जोड़ें।
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अनुक्रम \(45,40,35,30,\ldots\) में (0) कौन-सा पद है?
In the sequence \(45,40,35,30,\ldots\), which term is (0)?
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A (9)वाँ / (9)th
B (10)वाँ / (10)th
C (11)वाँ / (11)th
D (12)वाँ / (12)th
Explanation opens after your attempt
Correct Answer
B. (10)वाँ / (10)th
Step 1
Concept
The general term is \(a_n=50-5n\), and (50-5n=0) gives (n=10). Even in a decreasing sequence the position remains natural.
Step 2
Why this answer is correct
The correct answer is B. (10)वाँ / (10)th. The general term is \(a_n=50-5n\), and (50-5n=0) gives (n=10). Even in a decreasing sequence the position remains natural.
Step 3
Exam Tip
सामान्य पद \(a_n=50-5n\) है और (50-5n=0) से (n=10)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक रहती है।
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यदि \(a_n=2n^2+2n+1\) है तो पहले तीन पद कौन-से हैं?
If \(a_n=2n^2+2n+1\), what are the first three terms?
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A (3,9,19)
B (4,12,24)
C (5,11,21)
D (5,13,25)
Explanation opens after your attempt
Correct Answer
D. (5,13,25)
Step 1
Concept
Putting (n=1,2,3) gives (5,13,25). Calculate each term carefully in a quadratic rule.
Step 2
Why this answer is correct
The correct answer is D. (5,13,25). Putting (n=1,2,3) gives (5,13,25). Calculate each term carefully in a quadratic rule.
Step 3
Exam Tip
(n=1,2,3) रखने पर (5,13,25) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें।
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अनुक्रम \(\frac{2}{3},\frac{5}{4},\frac{10}{5},\frac{17}{6},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{2}{3},\frac{5}{4},\frac{10}{5},\frac{17}{6},\ldots\)?
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A \(a_n=\frac{n^2+1}{n+2}\)
B \(a_n=\frac{n^2+2}{n+1}\)
C \(a_n=\frac{2n+1}{n+2}\)
D \(a_n=\frac{n^2+n}{n+2}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{n^2+1}{n+2}\)
Step 1
Concept
The numerator is \(n^2+1\) and the denominator is (n+2), so \(a_n=\frac{n^2+1}{n+2}\). In a fractional sequence identify the numerator pattern separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{n^2+1}{n+2}\). The numerator is \(n^2+1\) and the denominator is (n+2), so \(a_n=\frac{n^2+1}{n+2}\). In a fractional sequence identify the numerator pattern separately.
Step 3
Exam Tip
अंश \(n^2+1\) और हर (n+2) है इसलिए \(a_n=\frac{n^2+1}{n+2}\)। भिन्न अनुक्रम में अंश का अलग पैटर्न पहचानें।
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यदि \(a_n=9n-4\) है तो \(a_8-a_3\) कितना होगा?
If \(a_n=9n-4\), what is \(a_8-a_3\)?
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#linear-rule
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A (40)
B (45)
C (50)
D (55)
Explanation opens after your attempt
Step 1
Concept
\(a_8=68\) and \(a_3=23\), so the difference is (45). Calculate both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (45). \(a_8=68\) and \(a_3=23\), so the difference is (45). Calculate both terms separately before subtracting.
Step 3
Exam Tip
\(a_8=68\) और \(a_3=23\), इसलिए अंतर (45) है। घटाने से पहले दोनों पदों की अलग गणना करें।
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यदि \(a_n=12-2n\) है तो पहला ऋणात्मक पद कौन-सा होगा?
If \(a_n=12-2n\), which will be the first negative term?
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A (6)वाँ / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
Explanation opens after your attempt
Correct Answer
B. (7)वाँ / (7)th
Step 1
Concept
\(a_6=0\) and \(a_7=-2\), so the first negative term is the (7)th. Do not count zero as negative.
Step 2
Why this answer is correct
The correct answer is B. (7)वाँ / (7)th. \(a_6=0\) and \(a_7=-2\), so the first negative term is the (7)th. Do not count zero as negative.
Step 3
Exam Tip
\(a_6=0\) और \(a_7=-2\) है, इसलिए पहला ऋणात्मक पद (7)वाँ है। शून्य को ऋणात्मक न मानें।
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एक समानांतर अनुक्रम में \(a_3=13\) और \(a_6=25\) है। \(a_9\) का मान क्या होगा?
In an arithmetic sequence, \(a_3=13\) and \(a_6=25\). What is the value of \(a_9\)?
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A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
The increase over three gaps is (12), so (d=4), hence (a_9=25+3(4)=37). Extend the terms using the common difference.
Step 2
Why this answer is correct
The correct answer is D. (37). The increase over three gaps is (12), so (d=4), hence (a_9=25+3(4)=37). Extend the terms using the common difference.
Step 3
Exam Tip
तीन अंतरों में वृद्धि (12) है इसलिए (d=4), अतः (a_9=25+3(4)=37)। समान अंतर को आगे बढ़ाकर पद निकालें।
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अनुक्रम \(2,9,28,65,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(2,9,28,65,\ldots\)?
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#progressions
#cube-sequence
#general-rule
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A \(a_n=n^3+1\)
B \(a_n=n^3-1\)
C (a_n=(n+1)3 )
D \(a_n=2n^3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^3+1\)
Step 1
Concept
This is \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\), so \(a_n=n^3+1\). In cube sequences identify the constant shift.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^3+1\). This is \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\), so \(a_n=n^3+1\). In cube sequences identify the constant shift.
Step 3
Exam Tip
यह \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\) है इसलिए \(a_n=n^3+1\)। घन अनुक्रम में स्थिर वृद्धि को पहचानें।
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यदि (a_n=\frac{n(n+1)}{2}) है तो \(a_n=45\) किस पद पर होगा?
If (a_n=\frac{n(n+1)}{2}), at which term will \(a_n=45\)?
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#progressions
#triangular-numbers
#term-position
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
C. (9)वाँ / (9)th
Step 1
Concept
Putting (n=9) gives \(\frac{9\cdot10}{2}=45\). Direct option checking is a quick method.
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. Putting (n=9) gives \(\frac{9\cdot10}{2}=45\). Direct option checking is a quick method.
Step 3
Exam Tip
(n=9) रखने पर \(\frac{9\cdot10}{2}=45\) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।
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अनुक्रम \(6,-9,12,-15,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(6,-9,12,-15,\ldots\)?
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#general-rule
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A (a_n=(-1)^n3(n+1))
B (a_n=(-1)^{n+1}3n)
C (a_n=(-1)^{n+1}3(n+1))
D \(a_n=3n+3\)
Explanation opens after your attempt
Correct Answer
C. (a_n=(-1)^{n+1}3(n+1))
Step 1
Concept
The magnitude is \(6,9,12,15,\ldots\) and signs alternate, so (a_n=(-1)^{n+1}3(n+1)). Use the first term sign to decide the power of ((-1)).
Step 2
Why this answer is correct
The correct answer is C. (a_n=(-1)^{n+1}3(n+1)). The magnitude is \(6,9,12,15,\ldots\) and signs alternate, so (a_n=(-1)^{n+1}3(n+1)). Use the first term sign to decide the power of ((-1)).
Step 3
Exam Tip
परिमाण \(6,9,12,15,\ldots\) है और चिह्न बदलता है इसलिए (a_n=(-1)^{n+1}3(n+1))। पहले पद के चिह्न से ((-1)) की शक्ति तय करें।
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यदि \(a_n=2n^2+n-1\) है तो \(a_6-a_2\) का मान क्या होगा?
If \(a_n=2n^2+n-1\), what is the value of \(a_6-a_2\)?
#sequences
#progressions
#quadratic-rule
#difference-of-terms
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A (64)
B (68)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_6=77\) and \(a_2=9\), so the difference is (68). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (68). \(a_6=77\) and \(a_2=9\), so the difference is (68). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_6=77\) और \(a_2=9\), इसलिए अंतर (68) है। घटाने से पहले दोनों पद अलग-अलग निकालें।
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