यदि किसी अनुक्रम का (n)वाँ पद \(a_n=n+8\) है, तो चौथा पद क्या होगा?
If the (n)th term of a sequence is \(a_n=n+8\), what is the fourth term?
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A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Putting (n=4) gives \(a_4=4+8=12\). In exams, replace (n) with the term number.
Step 2
Why this answer is correct
The correct answer is C. (12). Putting (n=4) gives \(a_4=4+8=12\). In exams, replace (n) with the term number.
Step 3
Exam Tip
(n=4) रखने पर \(a_4=4+8=12\) मिलता है। परीक्षा में (n) की जगह पद संख्या रखें।
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यदि \(a_n=4n\) है, तो ग्यारहवाँ पद क्या होगा?
If \(a_n=4n\), what is the eleventh term?
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A (40)
B (44)
C (48)
D (52)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=4\times11=44\). In exams, multiply by the term number in a multiples rule.
Step 2
Why this answer is correct
The correct answer is B. (44). \(a_{11}=4\times11=44\). In exams, multiply by the term number in a multiples rule.
Step 3
Exam Tip
\(a_{11}=4\times11=44\) है। परीक्षा में गुणज वाले नियम में पद संख्या से गुणा करें।
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यदि \(a_n=3n-1\) है, तो छठा पद क्या होगा?
If \(a_n=3n-1\), what is the sixth term?
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A (15)
B (16)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(a_6=3\times6-1=17\). In exams, multiply first and then subtract.
Step 2
Why this answer is correct
The correct answer is C. (17). \(a_6=3\times6-1=17\). In exams, multiply first and then subtract.
Step 3
Exam Tip
\(a_6=3\times6-1=17\) है। परीक्षा में पहले गुणा करें फिर घटाएँ।
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वर्ग संख्या अनुक्रम \(1,4,9,16,\ldots\) का आठवाँ पद क्या होगा?
What is the eighth term of the square number sequence \(1,4,9,16,\ldots\)?
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A (49)
B (56)
C (64)
D (81)
Explanation opens after your attempt
Step 1
Concept
Here \(a_n=n^2\), so \(a_8=8^2=64\). In exams, remember the square-number rule.
Step 2
Why this answer is correct
The correct answer is C. (64). Here \(a_n=n^2\), so \(a_8=8^2=64\). In exams, remember the square-number rule.
Step 3
Exam Tip
यहाँ \(a_n=n^2\) है, इसलिए \(a_8=8^2=64\) है। परीक्षा में वर्ग संख्या का नियम याद रखें।
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यदि \(a_n=n^2+3\) है, तो पाँचवाँ पद क्या होगा?
If \(a_n=n^2+3\), what is the fifth term?
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A (25)
B (27)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(a_5=5^2+3=28\). In exams, square first and then add the constant number.
Step 2
Why this answer is correct
The correct answer is C. (28). \(a_5=5^2+3=28\). In exams, square first and then add the constant number.
Step 3
Exam Tip
\(a_5=5^2+3=28\) है। परीक्षा में पहले वर्ग निकालें फिर स्थिर संख्या जोड़ें।
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अनुक्रम \(2,6,10,14,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(2,6,10,14,\ldots\)?
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A \(a_n=4n-2\)
B \(a_n=4n+2\)
C \(a_n=2n+4\)
D \(a_n=2n-4\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n-2\)
Step 1
Concept
The first term is (2) and the difference is (4), so \(a_n=4n-2\). In exams, check the first term by putting (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n-2\). The first term is (2) and the difference is (4), so \(a_n=4n-2\). In exams, check the first term by putting (n=1).
Step 3
Exam Tip
पहला पद (2) और अंतर (4) है, इसलिए \(a_n=4n-2\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।
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अनुक्रम \(8,16,24,32,\ldots\) में (72) कौन-सा पद है?
In the sequence \(8,16,24,32,\ldots\), which term is (72)?
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A सातवाँ पद / seventh term
B आठवाँ पद / eighth term
C नौवाँ पद / ninth term
D दसवाँ पद / tenth term
Explanation opens after your attempt
Correct Answer
C. नौवाँ पद / ninth term
Step 1
Concept
Here \(a_n=8n\), and (8n=72) gives (n=9). In exams, equate the given term to the general term.
Step 2
Why this answer is correct
The correct answer is C. नौवाँ पद / ninth term. Here \(a_n=8n\), and (8n=72) gives (n=9). In exams, equate the given term to the general term.
Step 3
Exam Tip
यहाँ \(a_n=8n\) है और (8n=72) से (n=9) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।
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यदि \(a_n=2^n\) है, तो छठा पद क्या होगा?
If \(a_n=2^n\), what is the sixth term?
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A (32)
B (48)
C (64)
D (128)
Explanation opens after your attempt
Step 1
Concept
\(a_6=2^6=64\). In exams, use the term number as the exponent in a power rule.
Step 2
Why this answer is correct
The correct answer is C. (64). \(a_6=2^6=64\). In exams, use the term number as the exponent in a power rule.
Step 3
Exam Tip
\(a_6=2^6=64\) है। परीक्षा में घात वाले नियम में पद संख्या को घात बनाइए।
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यदि \(a_n=10n-3\) है, तो दूसरा पद क्या होगा?
If \(a_n=10n-3\), what is the second term?
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A (15)
B (16)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(a_2=10\times2-3=17\). In exams, apply the full rule even for small terms.
Step 2
Why this answer is correct
The correct answer is C. (17). \(a_2=10\times2-3=17\). In exams, apply the full rule even for small terms.
Step 3
Exam Tip
\(a_2=10\times2-3=17\) है। परीक्षा में छोटे पदों पर भी पूरा नियम लगाएँ।
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अनुक्रम \(12,24,36,48,\ldots\) का सातवाँ पद क्या है?
What is the seventh term of the sequence \(12,24,36,48,\ldots\)?
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A (72)
B (84)
C (96)
D (108)
Explanation opens after your attempt
Step 1
Concept
Its rule is \(a_n=12n\), so \(a_7=84\). In exams, use the multiples rule.
Step 2
Why this answer is correct
The correct answer is B. (84). Its rule is \(a_n=12n\), so \(a_7=84\). In exams, use the multiples rule.
Step 3
Exam Tip
इसका नियम \(a_n=12n\) है, इसलिए \(a_7=84\) है। परीक्षा में गुणज वाले नियम का उपयोग करें।
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यदि \(a_n=18-n\) है, तो नौवाँ पद क्या होगा?
If \(a_n=18-n\), what is the ninth term?
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_9=18-9=9\). In exams, keep the order carefully in subtraction rules.
Step 2
Why this answer is correct
The correct answer is C. (9). \(a_9=18-9=9\). In exams, keep the order carefully in subtraction rules.
Step 3
Exam Tip
\(a_9=18-9=9\) है। परीक्षा में घटाने वाले नियम में क्रम ध्यान से रखें।
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अनुक्रम \(7,11,15,19,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(7,11,15,19,\ldots\)?
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A \(a_n=4n+3\)
B \(a_n=7n-3\)
C \(a_n=4n-3\)
D \(a_n=n+7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n+3\)
Step 1
Concept
The first term is (7) and the difference is (4), so \(a_n=4n+3\). In exams, match the rule at (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n+3\). The first term is (7) and the difference is (4), so \(a_n=4n+3\). In exams, match the rule at (n=1).
Step 3
Exam Tip
पहला पद (7) और अंतर (4) है, इसलिए \(a_n=4n+3\) है। परीक्षा में (n=1) पर नियम मिलाएँ।
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यदि \(a_n=6n+1\) है, तो \(a_8\) का मान क्या होगा?
If \(a_n=6n+1\), what is the value of \(a_8\)?
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A (47)
B (48)
C (49)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(a_8=6\times8+1=49\). In exams, add after multiplying.
Step 2
Why this answer is correct
The correct answer is C. (49). \(a_8=6\times8+1=49\). In exams, add after multiplying.
Step 3
Exam Tip
\(a_8=6\times8+1=49\) है। परीक्षा में गुणा के बाद जोड़ें।
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अनुक्रम \(1,3,5,7,\ldots\) में (31) कौन-सा पद है?
In the sequence \(1,3,5,7,\ldots\), which term is (31)?
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A चौदहवाँ पद / fourteenth term
B पंद्रहवाँ पद / fifteenth term
C सोलहवाँ पद / sixteenth term
D सत्रहवाँ पद / seventeenth term
Explanation opens after your attempt
Correct Answer
C. सोलहवाँ पद / sixteenth term
Step 1
Concept
Here \(a_n=2n-1\), and (2n-1=31) gives (n=16). In exams, remember the odd-number rule.
Step 2
Why this answer is correct
The correct answer is C. सोलहवाँ पद / sixteenth term. Here \(a_n=2n-1\), and (2n-1=31) gives (n=16). In exams, remember the odd-number rule.
Step 3
Exam Tip
यहाँ \(a_n=2n-1\) है और (2n-1=31) से (n=16) है। परीक्षा में विषम संख्या का नियम याद रखें।
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यदि \(a_n=n^3+1\) है, तो तीसरा पद क्या होगा?
If \(a_n=n^3+1\), what is the third term?
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A (26)
B (27)
C (28)
D (29)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3^3+1=28\). In exams, find the cube first and then add (1).
Step 2
Why this answer is correct
The correct answer is C. (28). \(a_3=3^3+1=28\). In exams, find the cube first and then add (1).
Step 3
Exam Tip
\(a_3=3^3+1=28\) है। परीक्षा में पहले घन निकालें फिर (1) जोड़ें।
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अनुक्रम \(3,12,27,48,\ldots\) के लिए कौन-सा (n)वाँ पद सही है?
Which (n)th term is correct for the sequence \(3,12,27,48,\ldots\)?
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A \(a_n=3n^2\)
B \(a_n=3n\)
C \(a_n=n^3\)
D \(a_n=3^n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2\)
Step 1
Concept
At (n=1,2,3,4), it gives (3,12,27,48). In exams, test options on the starting terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2\). At (n=1,2,3,4), it gives (3,12,27,48). In exams, test options on the starting terms.
Step 3
Exam Tip
(n=1,2,3,4) पर (3,12,27,48) मिलते हैं। परीक्षा में विकल्पों को शुरुआती पदों पर जाँचें।
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यदि \(a_n=\frac{n+3}{2}\) है, तो \(a_7\) का मान क्या होगा?
If \(a_n=\frac{n+3}{2}\), what is the value of \(a_7\)?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(a_7=\frac{7+3}{2}=5\). In exams, simplify the numerator first in fractional rules.
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_7=\frac{7+3}{2}=5\). In exams, simplify the numerator first in fractional rules.
Step 3
Exam Tip
\(a_7=\frac{7+3}{2}=5\) है। परीक्षा में भिन्न वाले नियम में पहले अंश सरल करें।
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अनुक्रम \(2,\frac{5}{2},3,\frac{7}{2},\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(2,\frac{5}{2},3,\frac{7}{2},\ldots\)?
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A \(a_n=\frac{n+3}{2}\)
B \(a_n=\frac{n}{2}\)
C \(a_n=2n\)
D \(a_n=n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{n+3}{2}\)
Step 1
Concept
At (n=1), it gives (2), and at (n=2), it gives \(\frac{5}{2}\). In exams, match a fractional rule with the first two terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{n+3}{2}\). At (n=1), it gives (2), and at (n=2), it gives \(\frac{5}{2}\). In exams, match a fractional rule with the first two terms.
Step 3
Exam Tip
(n=1) पर (2) और (n=2) पर \(\frac{5}{2}\) मिलता है। परीक्षा में भिन्न नियम को पहले दो पदों से मिलाएँ।
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यदि \(a_n=4^n\) है, तो दूसरा पद क्या होगा?
If \(a_n=4^n\), what is the second term?
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A (8)
B (12)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_2=4^2=16\). In exams, calculate the power carefully.
Step 2
Why this answer is correct
The correct answer is C. (16). \(a_2=4^2=16\). In exams, calculate the power carefully.
Step 3
Exam Tip
\(a_2=4^2=16\) है। परीक्षा में घात का मान ध्यान से निकालें।
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यदि \(a_n=8n-6\) है, तो पाँचवाँ पद क्या होगा?
If \(a_n=8n-6\), what is the fifth term?
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A (30)
B (32)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(a_5=8\times5-6=34\). In exams, multiply first and then subtract.
Step 2
Why this answer is correct
The correct answer is C. (34). \(a_5=8\times5-6=34\). In exams, multiply first and then subtract.
Step 3
Exam Tip
\(a_5=8\times5-6=34\) है। परीक्षा में पहले गुणा करें फिर घटाएँ।
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अनुक्रम \(6,13,20,27,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(6,13,20,27,\ldots\)?
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A \(a_n=7n-1\)
B \(a_n=7n+1\)
C \(a_n=6n+7\)
D \(a_n=n+6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7n-1\)
Step 1
Concept
The first term is (6) and the difference is (7), so \(a_n=7n-1\). In exams, check the first term at (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=7n-1\). The first term is (6) and the difference is (7), so \(a_n=7n-1\). In exams, check the first term at (n=1).
Step 3
Exam Tip
पहला पद (6) और अंतर (7) है, इसलिए \(a_n=7n-1\) है। परीक्षा में (n=1) पर पहला पद जाँचें।
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यदि \(a_n=25-2n\) है, तो सातवाँ पद क्या होगा?
If \(a_n=25-2n\), what is the seventh term?
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(a_7=25-2\times7=11\). In exams, multiply first in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is C. (11). \(a_7=25-2\times7=11\). In exams, multiply first in a decreasing sequence.
Step 3
Exam Tip
\(a_7=25-2\times7=11\) है। परीक्षा में घटती श्रेणी में गुणा पहले करें।
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अनुक्रम \(20,40,60,80,\ldots\) में (160) कौन-सा पद है?
In the sequence \(20,40,60,80,\ldots\), which term is (160)?
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A छठा पद / sixth term
B सातवाँ पद / seventh term
C आठवाँ पद / eighth term
D नौवाँ पद / ninth term
Explanation opens after your attempt
Correct Answer
C. आठवाँ पद / eighth term
Step 1
Concept
Here \(a_n=20n\), and (20n=160) gives (n=8). In exams, divide to find the term number.
Step 2
Why this answer is correct
The correct answer is C. आठवाँ पद / eighth term. Here \(a_n=20n\), and (20n=160) gives (n=8). In exams, divide to find the term number.
Step 3
Exam Tip
यहाँ \(a_n=20n\) है और (20n=160) से (n=8) है। परीक्षा में पद संख्या निकालने के लिए भाग दें।
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यदि \(a_n=\frac{5n}{2}\) है, तो चौथा पद क्या होगा?
If \(a_n=\frac{5n}{2}\), what is the fourth term?
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A (8)
B (10)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(a_4=\frac{5\times4}{2}=10\). In exams, simplify the fraction before writing the answer.
Step 2
Why this answer is correct
The correct answer is B. (10). \(a_4=\frac{5\times4}{2}=10\). In exams, simplify the fraction before writing the answer.
Step 3
Exam Tip
\(a_4=\frac{5\times4}{2}=10\) है। परीक्षा में भिन्न को सरल करके उत्तर लिखें।
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अनुक्रम \(\frac{5}{2},5,\frac{15}{2},10,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(\frac{5}{2},5,\frac{15}{2},10,\ldots\)?
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A \(a_n=\frac{5n}{2}\)
B \(a_n=\frac{n}{5}\)
C \(a_n=5n\)
D \(a_n=n+\frac{5}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{5n}{2}\)
Step 1
Concept
Each term is equal to \(\frac{5}{2}\) times (n). In exams, identify the fractional multiplier.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{5n}{2}\). Each term is equal to \(\frac{5}{2}\) times (n). In exams, identify the fractional multiplier.
Step 3
Exam Tip
हर पद (n) के \(\frac{5}{2}\) गुने के बराबर है। परीक्षा में भिन्न गुणक पहचानें।
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यदि \(a_n=3^n+2\) है, तो तीसरा पद क्या होगा?
If \(a_n=3^n+2\), what is the third term?
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A (27)
B (28)
C (29)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3^3+2=29\). In exams, calculate the power first and then add.
Step 2
Why this answer is correct
The correct answer is C. (29). \(a_3=3^3+2=29\). In exams, calculate the power first and then add.
Step 3
Exam Tip
\(a_3=3^3+2=29\) है। परीक्षा में पहले घात निकालें फिर जोड़ें।
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यदि \(a_n=50-5n\) है, तो छठा पद क्या होगा?
If \(a_n=50-5n\), what is the sixth term?
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A (15)
B (20)
C (25)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(a_6=50-5\times6=20\). In exams, keep the signs and order correct.
Step 2
Why this answer is correct
The correct answer is B. (20). \(a_6=50-5\times6=20\). In exams, keep the signs and order correct.
Step 3
Exam Tip
\(a_6=50-5\times6=20\) है। परीक्षा में चिह्न और क्रम सही रखें।
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अनुक्रम \(15,30,45,60,\ldots\) में (105) कौन-सा पद है?
In the sequence \(15,30,45,60,\ldots\), which term is (105)?
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A पाँचवाँ पद / fifth term
B छठा पद / sixth term
C सातवाँ पद / seventh term
D आठवाँ पद / eighth term
Explanation opens after your attempt
Correct Answer
C. सातवाँ पद / seventh term
Step 1
Concept
Here \(a_n=15n\), and (15n=105) gives (n=7). In exams, identify the multiple and find the term number.
Step 2
Why this answer is correct
The correct answer is C. सातवाँ पद / seventh term. Here \(a_n=15n\), and (15n=105) gives (n=7). In exams, identify the multiple and find the term number.
Step 3
Exam Tip
यहाँ \(a_n=15n\) है और (15n=105) से (n=7) है। परीक्षा में गुणज पहचानकर पद संख्या निकालें।
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यदि (a_n=n(n+2)) है, तो तीसरा पद क्या होगा?
If (a_n=n(n+2)), what is the third term?
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A (12)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
(a_3=3(3+2)=15). In exams, simplify inside the bracket first.
Step 2
Why this answer is correct
The correct answer is B. (15). (a_3=3(3+2)=15). In exams, simplify inside the bracket first.
Step 3
Exam Tip
(a_3=3(3+2)=15) है। परीक्षा में कोष्ठक के अंदर पहले सरल करें।
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अनुक्रम \(3,8,15,24,\ldots\) के लिए कौन-सा (n)वाँ पद सही है?
Which (n)th term is correct for the sequence \(3,8,15,24,\ldots\)?
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A (a_n=n(n+2))
B \(a_n=3n\)
C \(a_n=n^2\)
D \(a_n=2^n+1\)
Explanation opens after your attempt
Correct Answer
A. (a_n=n(n+2))
Step 1
Concept
At (n=1,2,3,4), it gives (3,8,15,24). In exams, test options on the starting terms.
Step 2
Why this answer is correct
The correct answer is A. (a_n=n(n+2)). At (n=1,2,3,4), it gives (3,8,15,24). In exams, test options on the starting terms.
Step 3
Exam Tip
(n=1,2,3,4) पर (3,8,15,24) मिलते हैं। परीक्षा में विकल्पों को शुरुआती पदों पर जाँचें।
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यदि \(a_n=14n\) है, तो \(a_6\) का मान क्या होगा?
If \(a_n=14n\), what is the value of \(a_6\)?
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A (70)
B (76)
C (84)
D (98)
Explanation opens after your attempt
Step 1
Concept
\(a_6=14\times6=84\). In exams, multiply by the term number.
Step 2
Why this answer is correct
The correct answer is C. (84). \(a_6=14\times6=84\). In exams, multiply by the term number.
Step 3
Exam Tip
\(a_6=14\times6=84\) है। परीक्षा में पद संख्या से गुणा करें।
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अनुक्रम \(11,22,33,44,\ldots\) में (99) कौन-सा पद है?
In the sequence \(11,22,33,44,\ldots\), which term is (99)?
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A सातवाँ पद / seventh term
B आठवाँ पद / eighth term
C नौवाँ पद / ninth term
D दसवाँ पद / tenth term
Explanation opens after your attempt
Correct Answer
C. नौवाँ पद / ninth term
Step 1
Concept
Here \(a_n=11n\), and (11n=99) gives (n=9). In exams, spot the multiple to find the term number.
Step 2
Why this answer is correct
The correct answer is C. नौवाँ पद / ninth term. Here \(a_n=11n\), and (11n=99) gives (n=9). In exams, spot the multiple to find the term number.
Step 3
Exam Tip
यहाँ \(a_n=11n\) है और (11n=99) से (n=9) है। परीक्षा में गुणज देखकर पद संख्या निकालें।
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यदि \(a_n=2n+9\) है, तो \(a_5\) का मान क्या होगा?
If \(a_n=2n+9\), what is the value of \(a_5\)?
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A (17)
B (18)
C (19)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(a_5=2\times5+9=19\). In exams, substitute the correct term number for (n).
Step 2
Why this answer is correct
The correct answer is C. (19). \(a_5=2\times5+9=19\). In exams, substitute the correct term number for (n).
Step 3
Exam Tip
\(a_5=2\times5+9=19\) है। परीक्षा में (n) की जगह सही पद संख्या रखें।
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अनुक्रम \(10,13,16,19,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(10,13,16,19,\ldots\)?
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A \(a_n=3n+7\)
B \(a_n=10n-7\)
C \(a_n=3n-7\)
D \(a_n=n+10\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n+7\)
Step 1
Concept
The first term is (10) and the difference is (3), so \(a_n=3n+7\). In exams, check the first term at (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n+7\). The first term is (10) and the difference is (3), so \(a_n=3n+7\). In exams, check the first term at (n=1).
Step 3
Exam Tip
पहला पद (10) और अंतर (3) है, इसलिए \(a_n=3n+7\) है। परीक्षा में (n=1) पर पहला पद जाँचें।
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यदि \(a_n=n^2+n+1\) है, तो चौथा पद क्या होगा?
If \(a_n=n^2+n+1\), what is the fourth term?
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A (19)
B (20)
C (21)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(a_4=4^2+4+1=21\). In exams, add both the square and the term number.
Step 2
Why this answer is correct
The correct answer is C. (21). \(a_4=4^2+4+1=21\). In exams, add both the square and the term number.
Step 3
Exam Tip
\(a_4=4^2+4+1=21\) है। परीक्षा में वर्ग और पद संख्या दोनों जोड़ें।
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अनुक्रम \(3,7,13,21,\ldots\) के लिए कौन-सा (n)वाँ पद सही है?
Which (n)th term is correct for the sequence \(3,7,13,21,\ldots\)?
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A \(a_n=n^2+n+1\)
B \(a_n=3n+1\)
C \(a_n=n^2\)
D \(a_n=2n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+n+1\)
Step 1
Concept
At (n=1,2,3,4), it gives (3,7,13,21). In exams, match the rule with the starting terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+n+1\). At (n=1,2,3,4), it gives (3,7,13,21). In exams, match the rule with the starting terms.
Step 3
Exam Tip
(n=1,2,3,4) पर (3,7,13,21) मिलते हैं। परीक्षा में नियम को शुरुआती पदों से मिलाएँ।
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यदि \(a_n=7n+7\) है, तो तीसरा पद क्या होगा?
If \(a_n=7n+7\), what is the third term?
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A (21)
B (28)
C (35)
D (42)
Explanation opens after your attempt
Step 1
Concept
\(a_3=7\times3+7=28\). In exams, do both multiplication and addition carefully.
Step 2
Why this answer is correct
The correct answer is B. (28). \(a_3=7\times3+7=28\). In exams, do both multiplication and addition carefully.
Step 3
Exam Tip
\(a_3=7\times3+7=28\) है। परीक्षा में गुणा और जोड़ दोनों सावधानी से करें।
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अनुक्रम \(14,28,42,56,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(14,28,42,56,\ldots\)?
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A \(a_n=14n\)
B \(a_n=28n\)
C \(a_n=n+14\)
D \(a_n=14n+14\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=14n\)
Step 1
Concept
Each term is a multiple of (14), so \(a_n=14n\). In exams, make the rule based on multiples.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=14n\). Each term is a multiple of (14), so \(a_n=14n\). In exams, make the rule based on multiples.
Step 3
Exam Tip
हर पद (14) का गुणज है, इसलिए \(a_n=14n\) है। परीक्षा में गुणजों के आधार पर नियम बनाएँ।
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यदि (a_n=\frac{n(n+1)}{2}) है, तो छठा पद क्या होगा?
If (a_n=\frac{n(n+1)}{2}), what is the sixth term?
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A (15)
B (18)
C (21)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(a_6=\frac{6\times7}{2}=21\). In exams, substitute the value of (n) first and simplify the fraction.
Step 2
Why this answer is correct
The correct answer is C. (21). \(a_6=\frac{6\times7}{2}=21\). In exams, substitute the value of (n) first and simplify the fraction.
Step 3
Exam Tip
\(a_6=\frac{6\times7}{2}=21\) है। परीक्षा में पहले (n) का मान रखकर भिन्न सरल करें।
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अनुक्रम \(1,3,6,10,\ldots\) में (21) कौन-सा पद है?
In the sequence \(1,3,6,10,\ldots\), which term is (21)?
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A पाँचवाँ पद / fifth term
B छठा पद / sixth term
C सातवाँ पद / seventh term
D आठवाँ पद / eighth term
Explanation opens after your attempt
Correct Answer
B. छठा पद / sixth term
Step 1
Concept
Its rule is (a_n=\frac{n(n+1)}{2}), and \(a_6=21\). In exams, recognize the triangular-number pattern.
Step 2
Why this answer is correct
The correct answer is B. छठा पद / sixth term. Its rule is (a_n=\frac{n(n+1)}{2}), and \(a_6=21\). In exams, recognize the triangular-number pattern.
Step 3
Exam Tip
इसका नियम (a_n=\frac{n(n+1)}{2}) है और \(a_6=21\) है। परीक्षा में त्रिभुज संख्या का पैटर्न पहचानें।
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यदि \(a_n=16n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=16n\), what is the value of \(a_4\)?
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A (48)
B (56)
C (64)
D (72)
Explanation opens after your attempt
Step 1
Concept
\(a_4=16\times4=64\). In exams, multiply by the term number.
Step 2
Why this answer is correct
The correct answer is C. (64). \(a_4=16\times4=64\). In exams, multiply by the term number.
Step 3
Exam Tip
\(a_4=16\times4=64\) है। परीक्षा में पद संख्या से गुणा करें।
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अनुक्रम \(16,32,48,64,\ldots\) में (112) कौन-सा पद है?
In the sequence \(16,32,48,64,\ldots\), which term is (112)?
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A पाँचवाँ पद / fifth term
B छठा पद / sixth term
C सातवाँ पद / seventh term
D आठवाँ पद / eighth term
Explanation opens after your attempt
Correct Answer
C. सातवाँ पद / seventh term
Step 1
Concept
Here \(a_n=16n\), and (16n=112) gives (n=7). In exams, identify the multiple and find the term number.
Step 2
Why this answer is correct
The correct answer is C. सातवाँ पद / seventh term. Here \(a_n=16n\), and (16n=112) gives (n=7). In exams, identify the multiple and find the term number.
Step 3
Exam Tip
यहाँ \(a_n=16n\) है और (16n=112) से (n=7) है। परीक्षा में गुणज पहचानकर पद संख्या निकालें।
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यदि \(a_n=5n^2\) है, तो तीसरा पद क्या होगा?
If \(a_n=5n^2\), what is the third term?
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A (30)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(a_3=5\times3^2=45\). In exams, square first and then multiply.
Step 2
Why this answer is correct
The correct answer is C. (45). \(a_3=5\times3^2=45\). In exams, square first and then multiply.
Step 3
Exam Tip
\(a_3=5\times3^2=45\) है। परीक्षा में पहले वर्ग निकालें फिर गुणा करें।
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अनुक्रम \(5,20,45,80,\ldots\) का (n)वाँ पद क्या है?
What is the (n)th term of the sequence \(5,20,45,80,\ldots\)?
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A \(a_n=5n^2\)
B \(a_n=5n\)
C \(a_n=n^2+5\)
D \(a_n=5^n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n^2\)
Step 1
Concept
At (n=1,2,3,4), it gives (5,20,45,80). In exams, recognize square-based multiples.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n^2\). At (n=1,2,3,4), it gives (5,20,45,80). In exams, recognize square-based multiples.
Step 3
Exam Tip
(n=1,2,3,4) पर (5,20,45,80) मिलते हैं। परीक्षा में वर्ग आधारित गुणजों को पहचानें।
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यदि \(a_n=2n^2-1\) है, तो चौथा पद क्या होगा?
If \(a_n=2n^2-1\), what is the fourth term?
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A (29)
B (30)
C (31)
D (33)
Explanation opens after your attempt
Step 1
Concept
\(a_4=2\times4^2-1=31\). In exams, square first, then multiply, and then subtract.
Step 2
Why this answer is correct
The correct answer is C. (31). \(a_4=2\times4^2-1=31\). In exams, square first, then multiply, and then subtract.
Step 3
Exam Tip
\(a_4=2\times4^2-1=31\) है। परीक्षा में वर्ग के बाद गुणा और फिर घटाना करें।
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अनुक्रम \(1,7,17,31,\ldots\) के लिए कौन-सा (n)वाँ पद सही है?
Which (n)th term is correct for the sequence \(1,7,17,31,\ldots\)?
#sequences
#progressions
#nth-term
#class-9
#easy
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A \(a_n=2n^2-1\)
B \(a_n=2n-1\)
C \(a_n=n^2+1\)
D \(a_n=3n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2n^2-1\)
Step 1
Concept
At (n=1,2,3,4), it gives (1,7,17,31). In exams, test options on the starting terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2n^2-1\). At (n=1,2,3,4), it gives (1,7,17,31). In exams, test options on the starting terms.
Step 3
Exam Tip
(n=1,2,3,4) पर (1,7,17,31) मिलते हैं। परीक्षा में विकल्पों को शुरुआती पदों पर जाँचें।
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यदि \(a_n=3n^2+2\) है, तो तीसरा पद क्या होगा?
If \(a_n=3n^2+2\), what is the third term?
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#nth-term
#class-9
#easy
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A (25)
B (27)
C (28)
D (29)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3\times3^2+2=29\). In exams, square first, then multiply and add.
Step 2
Why this answer is correct
The correct answer is D. (29). \(a_3=3\times3^2+2=29\). In exams, square first, then multiply and add.
Step 3
Exam Tip
\(a_3=3\times3^2+2=29\) है। परीक्षा में पहले वर्ग निकालें फिर गुणा और जोड़ करें।
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अनुक्रम \(5,14,29,50,\ldots\) के लिए कौन-सा (n)वाँ पद सही है?
Which (n)th term is correct for the sequence \(5,14,29,50,\ldots\)?
#sequences
#progressions
#nth-term
#class-9
#easy
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A \(a_n=3n^2+2\)
B \(a_n=5n-1\)
C \(a_n=n^2+4\)
D \(a_n=3n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+2\)
Step 1
Concept
At (n=1,2,3,4), it gives (5,14,29,50). In exams, match the rule with the starting terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+2\). At (n=1,2,3,4), it gives (5,14,29,50). In exams, match the rule with the starting terms.
Step 3
Exam Tip
(n=1,2,3,4) पर (5,14,29,50) मिलते हैं। परीक्षा में नियम को शुरुआती पदों से मिलाएँ।
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यदि (a_n=\frac{n(n+3)}{2}) है, तो चौथा पद क्या होगा?
If (a_n=\frac{n(n+3)}{2}), what is the fourth term?
#sequences
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#nth-term
#class-9
#easy
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
(a_4=\frac{4(4+3)}{2}=14). In exams, simplify the bracket first.
Step 2
Why this answer is correct
The correct answer is C. (14). (a_4=\frac{4(4+3)}{2}=14). In exams, simplify the bracket first.
Step 3
Exam Tip
(a_4=\frac{4(4+3)}{2}=14) है। परीक्षा में कोष्ठक पहले सरल करें।
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अनुक्रम \(2,5,9,14,\ldots\) में पाँचवाँ पद क्या होगा?
What will be the fifth term in the sequence \(2,5,9,14,\ldots\)?
#sequences
#progressions
#nth-term
#class-9
#easy
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A (20)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
The differences (3,4,5) are increasing, so the next difference is (6) and the fifth term is (20). In exams, observe changing differences in order.
Step 2
Why this answer is correct
The correct answer is A. (20). The differences (3,4,5) are increasing, so the next difference is (6) and the fifth term is (20). In exams, observe changing differences in order.
Step 3
Exam Tip
अंतर (3,4,5) बढ़ रहे हैं, इसलिए अगला अंतर (6) और पाँचवाँ पद (20) है। परीक्षा में बदलते अंतर को क्रम से देखें।
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