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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#quadratic-sequence
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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 \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\frac{5}{9},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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))?
#sequences
#progressions
#product-pattern
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#geometric-sequence
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(9,16,25,36,\ldots\) का स्पष्ट नियम कौन-सा है?
Which is the explicit rule of the sequence \(9,16,25,36,\ldots\)?
#sequences
#progressions
#squares
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=n^2\)
B (a_n=(n+1)2 )
C \(a_n=n^2+8\)
D (a_n=(n+2)2 )
Explanation opens after your attempt
Correct Answer
D. (a_n=(n+2)2 )
Step 1
Concept
This is \(3^2,4^2,5^2,6^2,\ldots\), so (a_n=(n+2)2 ). In square sequences relate the base number to (n).
Step 2
Why this answer is correct
The correct answer is D. (a_n=(n+2)2 ). This is \(3^2,4^2,5^2,6^2,\ldots\), so (a_n=(n+2)2 ). In square sequences relate the base number to (n).
Step 3
Exam Tip
यह \(3^2,4^2,5^2,6^2,\ldots\) है इसलिए (a_n=(n+2)2 )। वर्ग अनुक्रम में आधार संख्या और (n) का संबंध देखें।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(1,-2,3,-4,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,-2,3,-4,\ldots\)?
#sequences
#progressions
#alternating-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(1,8,27,64,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(1,8,27,64,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=2n+1\) और \(b_n=n^2-1\) है तो \(a_4+b_4\) कितना होगा?
If \(a_n=2n+1\) and \(b_n=n^2-1\), what is \(a_4+b_4\)?
#sequences
#progressions
#combined-rules
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (20)
B (24)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(a_4=9\) and \(b_4=15\), so the sum is (24). When there are two rules use the same (n) in both.
Step 2
Why this answer is correct
The correct answer is B. (24). \(a_4=9\) and \(b_4=15\), so the sum is (24). When there are two rules use the same (n) in both.
Step 3
Exam Tip
\(a_4=9\) और \(b_4=15\) इसलिए योग (24) है। दो नियम हों तो दोनों में वही (n) रखें।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(5,11,19,29,\ldots\) का (8)वाँ पद क्या होगा?
What will be the (8)th term of the sequence \(5,11,19,29,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#nth-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(2,7,14,23,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(2,7,14,23,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=n^2+2n-1\)
B \(a_n=n^2+n\)
C \(a_n=2n^2+1\)
D \(a_n=n^2+3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+2n-1\)
Step 1
Concept
\(n^2+2n-1\) gives (2,7,14,23). When differences increase, check a quadratic rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+2n-1\). \(n^2+2n-1\) gives (2,7,14,23). When differences increase, check a quadratic rule.
Step 3
Exam Tip
\(n^2+2n-1\) से (2,7,14,23) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम की जांच करें।
Login to save your score, XP, coins and progress. Login
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 \(8,12,16,20,\ldots\)?
#sequences
#progressions
#term-checking
#arithmetic-sequence
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(1,9,25,49,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,9,25,49,\ldots\)?
#sequences
#progressions
#odd-squares
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=5^n\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=5^n\), what is the value of \(a_4\)?
#sequences
#progressions
#exponential-sequence
#nth-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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 \(\frac{1}{2},\frac{3}{3},\frac{5}{4},\frac{7}{5},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#arithmetic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
किस विकल्प में \(a_n=n^2+3n-1\) से बने पहले तीन पद हैं?
Which option contains the first three terms formed by \(a_n=n^2+3n-1\)?
#sequences
#progressions
#sequence-from-rule
#quadratic-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=kn+2\) और \(a_7=37\) है तो (k) का मान क्या है?
If \(a_n=kn+2\) and \(a_7=37\), what is the value of (k)?
#sequences
#progressions
#unknown-coefficient
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (4)
C (6)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (7k+2=37), (7k=35) and (k=5). Substitute the given term to find the unknown coefficient.
Step 2
Why this answer is correct
The correct answer is D. (5). From (7k+2=37), (7k=35) and (k=5). Substitute the given term to find the unknown coefficient.
Step 3
Exam Tip
(7k+2=37) से (7k=35) और (k=5)। अज्ञात गुणांक निकालने के लिए दिया पद substitute करें।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#explicit-rule
#word-problem
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(3,7,13,21,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(3,7,13,21,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=n^2+2\)
B \(a_n=n^2+n+1\)
C \(a_n=2n^2+1\)
D \(a_n=n^2+2n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+n+1\)
Step 1
Concept
\(n^2+n+1\) gives (3,7,13,21). Start checking quadratic options from (n=1).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+n+1\). \(n^2+n+1\) gives (3,7,13,21). Start checking quadratic options from (n=1).
Step 3
Exam Tip
\(n^2+n+1\) से (3,7,13,21) मिलते हैं। द्विघात विकल्पों को (n=1) से जांचना शुरू करें।
Login to save your score, XP, coins and progress. Login
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 \(a_n=\frac{5}{7}\)?
#sequences
#progressions
#fraction-sequence
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(0,3,8,15,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(0,3,8,15,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=n^2+1\)
B \(a_n=n^2-1\)
C \(a_n=2n-2\)
D \(a_n=n^2+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2-1\)
Step 1
Concept
\(n^2-1\) gives (0,3,8,15). If the second difference is constant, check a quadratic rule.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2-1\). \(n^2-1\) gives (0,3,8,15). If the second difference is constant, check a quadratic rule.
Step 3
Exam Tip
\(n^2-1\) से (0,3,8,15) मिलते हैं। यदि दूसरा अंतर स्थिर हो तो द्विघात नियम जांचें।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#exponential-sequence
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(-3,5,-7,9,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(-3,5,-7,9,\ldots\)?
#sequences
#progressions
#alternating-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(7,13,19,25,\ldots\) का (25)वाँ पद क्या है?
What is the (25)th term of the sequence \(7,13,19,25,\ldots\)?
#sequences
#progressions
#arithmetic-sequence
#nth-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
एक समानांतर अनुक्रम में \(a_1=8\) और \(a_4=20\) है। उसका स्पष्ट नियम क्या है?
In an arithmetic sequence, \(a_1=8\) and \(a_4=20\). What is its explicit rule?
#sequences
#progressions
#arithmetic-sequence
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=4n+8\)
B \(a_n=4n+4\)
C \(a_n=5n+3\)
D \(a_n=3n+5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n+4\)
Step 1
Concept
\(a_4-a_1=12\) and there are three gaps, so (d=4), hence (a_n=8+(n-1)4=4n+4). Find the common difference first.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n+4\). \(a_4-a_1=12\) and there are three gaps, so (d=4), hence (a_n=8+(n-1)4=4n+4). Find the common difference first.
Step 3
Exam Tip
\(a_4-a_1=12\) और तीन अंतर हैं इसलिए (d=4), अतः (a_n=8+(n-1)4=4n+4)। पहले समान अंतर निकालें।
Login to save your score, XP, coins and progress. Login
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 \(a_n=80\)?
#sequences
#progressions
#quadratic-rule
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(1,2,5,10,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,2,5,10,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=\frac{2n+3}{n+1}\) है तो \(a_4\) क्या होगा?
If \(a_n=\frac{2n+3}{n+1}\), what is \(a_4\)?
#sequences
#progressions
#fraction-rule
#nth-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(8,27,64,125,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(8,27,64,125,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(6,14,24,36,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(6,14,24,36,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=n^2+4n\)
B \(a_n=2n^2+4\)
C \(a_n=n^2+6n-1\)
D \(a_n=n^2+5n\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=n^2+5n\)
Step 1
Concept
\(n^2+5n\) gives (6,14,24,36). Check the options using (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is D. \(a_n=n^2+5n\). \(n^2+5n\) gives (6,14,24,36). Check the options using (n=1,2,3).
Step 3
Exam Tip
\(n^2+5n\) से (6,14,24,36) मिलते हैं। विकल्पों को (n=1,2,3) से जांचें।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=7-3n\) है तो इस अनुक्रम का समान अंतर क्या है?
If \(a_n=7-3n\), what is the common difference of this sequence?
#sequences
#progressions
#common-difference
#linear-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-3)
B (3)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
In a linear rule the coefficient of (n) is (-3), so the common difference is (-3). Read the coefficient of \(a_n\) carefully.
Step 2
Why this answer is correct
The correct answer is A. (-3). In a linear rule the coefficient of (n) is (-3), so the common difference is (-3). Read the coefficient of \(a_n\) carefully.
Step 3
Exam Tip
रैखिक नियम में (n) का गुणांक (-3) है इसलिए समान अंतर (-3) है। \(a_n\) के गुणांक को ध्यान से पढ़ें।
Login to save your score, XP, coins and progress. Login
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 \(a_5+a_1\)?
#sequences
#progressions
#sum-of-terms
#quadratic-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(45,40,35,30,\ldots\) में (0) कौन-सा पद है?
In the sequence \(45,40,35,30,\ldots\), which term is (0)?
#sequences
#progressions
#decreasing-sequence
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#sequence-from-rule
#quadratic-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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 \(\frac{2}{3},\frac{5}{4},\frac{10}{5},\frac{17}{6},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(\frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{4}{9},\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(\frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{4}{9},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=\frac{n+1}{2n+1}\)
B \(a_n=\frac{n}{n+2}\)
C \(a_n=\frac{n}{2n+1}\)
D \(a_n=\frac{2n-1}{n+2}\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=\frac{n}{2n+1}\)
Step 1
Concept
The numerator is (n) and the denominator is (2n+1), so \(a_n=\frac{n}{2n+1}\). In fractions observe the denominator growth carefully.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=\frac{n}{2n+1}\). The numerator is (n) and the denominator is (2n+1), so \(a_n=\frac{n}{2n+1}\). In fractions observe the denominator growth carefully.
Step 3
Exam Tip
अंश (n) और हर (2n+1) है इसलिए \(a_n=\frac{n}{2n+1}\)। भिन्नों में हर की बढ़त को ध्यान से देखें।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=9n-4\) है तो \(a_8-a_3\) कितना होगा?
If \(a_n=9n-4\), what is \(a_8-a_3\)?
#sequences
#progressions
#difference-of-terms
#linear-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(5,14,29,50,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(5,14,29,50,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=3n^2+2\)
B \(a_n=2n^2+3\)
C \(a_n=n^2+4n\)
D \(a_n=3n^2+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+2\)
Step 1
Concept
\(3n^2+2\) gives (5,14,29,50). Match the options with the initial terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+2\). \(3n^2+2\) gives (5,14,29,50). Match the options with the initial terms.
Step 3
Exam Tip
\(3n^2+2\) से (5,14,29,50) मिलते हैं। विकल्पों को शुरुआती पदों से मिलाएं।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=n^2+cn\) और \(a_3=18\) है तो (c) का मान क्या है?
If \(a_n=n^2+cn\) and \(a_3=18\), what is the value of (c)?
#sequences
#progressions
#unknown-coefficient
#quadratic-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (9+3c=18), (3c=9) and (c=3). Substitute the given term to find the unknown constant.
Step 2
Why this answer is correct
The correct answer is C. (3). From (9+3c=18), (3c=9) and (c=3). Substitute the given term to find the unknown constant.
Step 3
Exam Tip
(9+3c=18) से (3c=9) और (c=3)। अज्ञात स्थिरांक के लिए दिया पद रखें।
Login to save your score, XP, coins and progress. Login
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?
#sequences
#progressions
#decreasing-sequence
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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 \(a_9\)?
#sequences
#progressions
#arithmetic-sequence
#nth-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(2,9,28,65,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(2,9,28,65,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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 \(a_n=45\)?
#sequences
#progressions
#triangular-numbers
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
अनुक्रम \(6,-9,12,-15,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(6,-9,12,-15,\ldots\)?
#sequences
#progressions
#alternating-sequence
#general-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
एक समानांतर अनुक्रम में \(a_4=18\) और समान अंतर (5) है। स्पष्ट नियम क्या होगा?
In an arithmetic sequence, \(a_4=18\) and the common difference is (5). What will be the explicit rule?
#sequences
#progressions
#arithmetic-sequence
#explicit-rule
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(a_n=5n-2\)
B \(a_n=5n+2\)
C \(a_n=4n+2\)
D \(a_n=18+5n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n-2\)
Step 1
Concept
(a_1=18-3(5)=3), so (a_n=3+(n-1)5=5n-2). From a middle term first find the first term.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n-2\). (a_1=18-3(5)=3), so (a_n=3+(n-1)5=5n-2). From a middle term first find the first term.
Step 3
Exam Tip
(a_1=18-3(5)=3) इसलिए (a_n=3+(n-1)5=5n-2)। दिए हुए बीच के पद से पहले पहला पद निकालें।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
