यदि \(a_1=6\) और \(a_{n+1}=2a_n+n\) है तो \(a_4\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=2a_n+n\), what is \(a_4\)?
#recursive-rule
#double-plus-index
#class-9
#hard
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A (55)
B (57)
C (59)
D (61)
Explanation opens after your attempt
Step 1
Concept
The terms are (6,13,28,59), so \(a_4=59\). Exam tip: double the previous term and add (n).
Step 2
Why this answer is correct
The correct answer is C. (59). The terms are (6,13,28,59), so \(a_4=59\). Exam tip: double the previous term and add (n).
Step 3
Exam Tip
पद (6,13,28,59) हैं इसलिए \(a_4=59\) है। पिछले पद को दोगुना करके (n) जोड़ें।
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यदि \(a_1=80\) और (a_{n+1}=a_n-(3n+2)) है तो \(a_5\) क्या होगा?
If \(a_1=80\) and (a_{n+1}=a_n-(3n+2)), what is \(a_5\)?
#recursive-rule
#linear-decrement
#class-9
#hard
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A (38)
B (42)
C (46)
D (50)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (5,8,11,14), so \(a_5=42\). Exam tip: list the subtractions in order.
Step 2
Why this answer is correct
The correct answer is B. (42). The subtracted values are (5,8,11,14), so \(a_5=42\). Exam tip: list the subtractions in order.
Step 3
Exam Tip
घटने वाले मान (5,8,11,14) हैं इसलिए \(a_5=42\) है। घटावों को क्रम से लिखना सुरक्षित रहता है।
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यदि \(a_1=1\) और \(a_{n+1}=a_n+n^2+3n\) है तो \(a_5\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=a_n+n^2+3n\), what is \(a_5\)?
#recursive-rule
#quadratic-increment
#class-9
#hard
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A (61)
B (63)
C (65)
D (67)
Explanation opens after your attempt
Step 1
Concept
The added values are (4,10,18,28), so \(a_5=61\). Exam tip: first find the values of \(n^2+3n\).
Step 2
Why this answer is correct
The correct answer is A. (61). The added values are (4,10,18,28), so \(a_5=61\). Exam tip: first find the values of \(n^2+3n\).
Step 3
Exam Tip
जुड़ने वाले मान (4,10,18,28) हैं इसलिए \(a_5=61\) है। पहले \(n^2+3n\) के मान अलग निकालें।
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यदि \(a_1=100\) और (a_{n+1}=a_n-(n+1)2 ) है तो \(a_4\) क्या होगा?
If \(a_1=100\) and (a_{n+1}=a_n-(n+1)2 ), what is \(a_4\)?
#recursive-rule
#square-decrement
#class-9
#hard
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A (65)
B (68)
C (71)
D (74)
Explanation opens after your attempt
Step 1
Concept
The subtracted squares are (4,9,16), so (100-29=71). Exam tip: subtract squares in order.
Step 2
Why this answer is correct
The correct answer is C. (71). The subtracted squares are (4,9,16), so (100-29=71). Exam tip: subtract squares in order.
Step 3
Exam Tip
घटने वाले वर्ग (4,9,16) हैं इसलिए (100-29=71) है। वर्गों को क्रम से घटाएँ।
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}+a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=2a_{n-1}+a_{n-2}\), what is \(a_5\)?
#recursive-rule
#two-term-recurrence
#class-9
#hard
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A (62)
B (66)
C (70)
D (74)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,12,29,70), so \(a_5=70\). Exam tip: use both previous terms in a two-term rule.
Step 2
Why this answer is correct
The correct answer is C. (70). The terms are (2,5,12,29,70), so \(a_5=70\). Exam tip: use both previous terms in a two-term rule.
Step 3
Exam Tip
पद (2,5,12,29,70) हैं इसलिए \(a_5=70\) है। दो-पद नियम में दोनों पिछले पदों का उपयोग करें।
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यदि \(a_1=3\), \(a_2=7\) और \(a_n=3a_{n-1}-2a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=3\), \(a_2=7\), and \(a_n=3a_{n-1}-2a_{n-2}\), what is \(a_5\)?
#recursive-rule
#second-order
#class-9
#hard
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A (57)
B (60)
C (63)
D (66)
Explanation opens after your attempt
Step 1
Concept
The terms are (3,7,15,31,63), so \(a_5=63\). Exam tip: do not change the order of multiplication and subtraction.
Step 2
Why this answer is correct
The correct answer is C. (63). The terms are (3,7,15,31,63), so \(a_5=63\). Exam tip: do not change the order of multiplication and subtraction.
Step 3
Exam Tip
पद (3,7,15,31,63) हैं इसलिए \(a_5=63\) है। गुणा और घटाव का क्रम न बदलें।
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यदि \(a_1=4\) और \(a_{n+1}=a_n+2^n+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+2^n+n^2\), what is \(a_4\)?
#recursive-rule
#power-plus-square
#class-9
#hard
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A (26)
B (29)
C (32)
D (35)
Explanation opens after your attempt
Step 1
Concept
The added values are (3,8,17), so \(a_4=32\). Exam tip: calculate the power and square separately.
Step 2
Why this answer is correct
The correct answer is C. (32). The added values are (3,8,17), so \(a_4=32\). Exam tip: calculate the power and square separately.
Step 3
Exam Tip
जुड़ने वाले मान (3,8,17) हैं इसलिए \(a_4=32\) है। घात और वर्ग दोनों अलग-अलग निकालें।
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यदि \(a_1=120\) और (a_{n+1}=a_n-\(2^n+n\)) है तो \(a_5\) क्या होगा?
If \(a_1=120\) and (a_{n+1}=a_n-\(2^n+n\)), what is \(a_5\)?
#recursive-rule
#power-plus-index
#class-9
#hard
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A (76)
B (78)
C (80)
D (82)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (3,6,11,20), so \(a_5=80\). Exam tip: write values of \(2^n+n\) first.
Step 2
Why this answer is correct
The correct answer is C. (80). The subtracted values are (3,6,11,20), so \(a_5=80\). Exam tip: write values of \(2^n+n\) first.
Step 3
Exam Tip
घटने वाले मान (3,6,11,20) हैं इसलिए \(a_5=80\) है। \(2^n+n\) के मान पहले लिखें।
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यदि \(a_1=10\) और (a_{n+1}=a_n+(-1)^{n+1}(n+2)) है तो \(a_5\) क्या होगा?
If \(a_1=10\) and (a_{n+1}=a_n+(-1)^{n+1}(n+2)), what is \(a_5\)?
#recursive-rule
#alternating-index
#class-9
#hard
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A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
The terms are (10,13,9,14,8), so \(a_5=8\). Exam tip: check the sign at each step in alternating rules.
Step 2
Why this answer is correct
The correct answer is B. (8). The terms are (10,13,9,14,8), so \(a_5=8\). Exam tip: check the sign at each step in alternating rules.
Step 3
Exam Tip
पद (10,13,9,14,8) हैं इसलिए \(a_5=8\) है। चिह्न बदलने वाले नियम में हर चरण का संकेत देखें।
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यदि \(a_1=5\) और (a_{n+1}=a_n+n(n+2)+1) है तो \(a_4\) क्या होगा?
If \(a_1=5\) and (a_{n+1}=a_n+n(n+2)+1), what is \(a_4\)?
#recursive-rule
#product-increment
#class-9
#hard
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A (30)
B (32)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
The added values are (4,9,16), so \(a_4=34\). Exam tip: calculate the product first and then add (1).
Step 2
Why this answer is correct
The correct answer is C. (34). The added values are (4,9,16), so \(a_4=34\). Exam tip: calculate the product first and then add (1).
Step 3
Exam Tip
जुड़ने वाले मान (4,9,16) हैं इसलिए \(a_4=34\) है। पहले गुणनफल निकालें फिर (1) जोड़ें।
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यदि \(a_1=150\) और (a_{n+1}=a_n-n(n+2)-1) है तो \(a_4\) क्या होगा?
If \(a_1=150\) and (a_{n+1}=a_n-n(n+2)-1), what is \(a_4\)?
#recursive-rule
#product-decrement
#class-9
#hard
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A (115)
B (118)
C (121)
D (124)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (4,9,16), so \(a_4=121\). Exam tip: calculate the full subtraction before subtracting.
Step 2
Why this answer is correct
The correct answer is C. (121). The subtracted values are (4,9,16), so \(a_4=121\). Exam tip: calculate the full subtraction before subtracting.
Step 3
Exam Tip
घटने वाले मान (4,9,16) हैं इसलिए \(a_4=121\) है। पूरा घटाव निकालकर ही घटाएँ।
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यदि \(a_1=2\) और \(a_{n+1}=2a_n+3n-1\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=2a_n+3n-1\), what is \(a_4\)?
#recursive-rule
#double-plus-linear
#class-9
#hard
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A (36)
B (39)
C (42)
D (45)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,6,17,42), so \(a_4=42\). Exam tip: (3n-1) changes at every step.
Step 2
Why this answer is correct
The correct answer is C. (42). The terms are (2,6,17,42), so \(a_4=42\). Exam tip: (3n-1) changes at every step.
Step 3
Exam Tip
पद (2,6,17,42) हैं इसलिए \(a_4=42\) है। (3n-1) का मान हर चरण में नया होता है।
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यदि \(a_1=64\) और \(a_{n+1}=\frac{a_n}{2}+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=64\) and \(a_{n+1}=\frac{a_n}{2}+n^2\), what is \(a_3\)?
#recursive-rule
#half-plus-square
#class-9
#hard
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A \(\frac{39}{2}\)
B \(\frac{41}{2}\)
C \(\frac{43}{2}\)
D \(\frac{45}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{41}{2}\)
Step 1
Concept
\(a_2=32+1=33\) and \(a_3=\frac{33}{2}+4=\frac{41}{2}\). Exam tip: keep fractions exact until the end.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{41}{2}\). \(a_2=32+1=33\) and \(a_3=\frac{33}{2}+4=\frac{41}{2}\). Exam tip: keep fractions exact until the end.
Step 3
Exam Tip
\(a_2=32+1=33\) और \(a_3=\frac{33}{2}+4=\frac{41}{2}\) है। भिन्न को अंत तक सही रखें।
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यदि \(a_1=12\) और \(a_{n+1}=\frac{a_n}{3}+2n\) है तो \(a_3\) क्या होगा?
If \(a_1=12\) and \(a_{n+1}=\frac{a_n}{3}+2n\), what is \(a_3\)?
#recursive-rule
#third-plus-index
#class-9
#hard
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(a_2=\frac{12}{3}+2=6\) and \(a_3=\frac{6}{3}+4=6\). Exam tip: divide first and then add (2n).
Step 2
Why this answer is correct
The correct answer is C. (6). \(a_2=\frac{12}{3}+2=6\) and \(a_3=\frac{6}{3}+4=6\). Exam tip: divide first and then add (2n).
Step 3
Exam Tip
\(a_2=\frac{12}{3}+2=6\) और \(a_3=\frac{6}{3}+4=6\) है। पहले भाग करें फिर (2n) जोड़ें।
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यदि \(a_1=1\), \(a_2=4\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_5\) क्या होगा?
If \(a_1=1\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_5\)?
#recursive-rule
#two-term-plus-index
#class-9
#hard
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A (25)
B (27)
C (29)
D (31)
Explanation opens after your attempt
Step 1
Concept
The terms are (1,4,8,16,29), so \(a_5=29\). Exam tip: add the current (n) with the previous two terms.
Step 2
Why this answer is correct
The correct answer is C. (29). The terms are (1,4,8,16,29), so \(a_5=29\). Exam tip: add the current (n) with the previous two terms.
Step 3
Exam Tip
पद (1,4,8,16,29) हैं इसलिए \(a_5=29\) है। पिछले दो पदों के साथ वर्तमान (n) जोड़ें।
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यदि \(a_1=2\) और \(a_{n+1}=a_n^2+a_n+1\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n^2+a_n+1\), what is \(a_3\)?
#recursive-rule
#nonlinear-recurrence
#class-9
#hard
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A (53)
B (55)
C (57)
D (59)
Explanation opens after your attempt
Step 1
Concept
\(a_2=4+2+1=7\) and \(a_3=49+7+1=57\). Exam tip: square first, then add the previous term and (1).
Step 2
Why this answer is correct
The correct answer is C. (57). \(a_2=4+2+1=7\) and \(a_3=49+7+1=57\). Exam tip: square first, then add the previous term and (1).
Step 3
Exam Tip
\(a_2=4+2+1=7\) और \(a_3=49+7+1=57\) है। पहले वर्ग करें फिर पिछले पद और (1) जोड़ें।
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यदि \(a_1=6\) और \(a_{n+1}=a_n^2-4a_n\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n^2-4a_n\), what is \(a_3\)?
#recursive-rule
#nonlinear-recurrence
#class-9
#hard
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A (84)
B (90)
C (96)
D (102)
Explanation opens after your attempt
Step 1
Concept
\(a_2=36-24=12\) and \(a_3=144-48=96\). Exam tip: square the previous term and subtract four times it.
Step 2
Why this answer is correct
The correct answer is C. (96). \(a_2=36-24=12\) and \(a_3=144-48=96\). Exam tip: square the previous term and subtract four times it.
Step 3
Exam Tip
\(a_2=36-24=12\) और \(a_3=144-48=96\) है। पिछले पद का वर्ग लेकर उसका (4) गुना घटाएँ।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+4\) है तो कौन सा पद (53) है?
If \(a_1=9\) and \(a_{n+1}=a_n+4\), which term is (53)?
#recursive-rule
#term-position
#class-9
#hard
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A (10)वाँ / (10)th
B (11)वाँ / (11)th
C (12)वाँ / (12)th
D (13)वाँ / (13)th
Explanation opens after your attempt
Correct Answer
C. (12)वाँ / (12)th
Step 1
Concept
(53-9=44), and \(44\div4=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.
Step 2
Why this answer is correct
The correct answer is C. (12)वाँ / (12)th. (53-9=44), and \(44\div4=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.
Step 3
Exam Tip
(53-9=44) और \(44\div4=11\) चरण हैं इसलिए पद संख्या (12) है। चरणों में (1) जोड़कर पद संख्या मिलती है।
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यदि \(a_1=7\) और \(a_{n+1}=a_n+6\) है तो \(a_{10}\) क्या होगा?
If \(a_1=7\) and \(a_{n+1}=a_n+6\), what is \(a_{10}\)?
#recursive-rule
#constant-add
#class-9
#hard
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A (55)
B (58)
C (61)
D (64)
Explanation opens after your attempt
Step 1
Concept
For \(a_{10}\), (6) is added (9) times, so (7+54=61). Exam tip: the rule is applied one less time than the term number.
Step 2
Why this answer is correct
The correct answer is C. (61). For \(a_{10}\), (6) is added (9) times, so (7+54=61). Exam tip: the rule is applied one less time than the term number.
Step 3
Exam Tip
\(a_{10}\) के लिए (6) को (9) बार जोड़ा जाता है इसलिए (7+54=61) है। पद संख्या से एक कम बार नियम लगता है।
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यदि \(a_1=3\) और \(a_{n+1}=2a_n+5\) है तो \(a_4-a_2\) का मान क्या होगा?
If \(a_1=3\) and \(a_{n+1}=2a_n+5\), what is the value of \(a_4-a_2\)?
#recursive-rule
#difference-of-terms
#class-9
#hard
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A (42)
B (45)
C (48)
D (51)
Explanation opens after your attempt
Step 1
Concept
The terms are (3,11,27,59), so \(a_4-a_2=48\). Exam tip: find both terms first and subtract.
Step 2
Why this answer is correct
The correct answer is C. (48). The terms are (3,11,27,59), so \(a_4-a_2=48\). Exam tip: find both terms first and subtract.
Step 3
Exam Tip
पद (3,11,27,59) हैं इसलिए \(a_4-a_2=48\) है। पहले दोनों पद निकालकर घटाएँ।
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यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+5\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+5\), what is \(a_5\)?
#recursive-rule
#two-term-plus-constant
#class-9
#hard
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A (34)
B (38)
C (42)
D (46)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,6,13,24,42), so \(a_5=42\). Exam tip: add (5) along with the previous two terms.
Step 2
Why this answer is correct
The correct answer is C. (42). The terms are (2,6,13,24,42), so \(a_5=42\). Exam tip: add (5) along with the previous two terms.
Step 3
Exam Tip
पद (2,6,13,24,42) हैं इसलिए \(a_5=42\) है। पिछले दो पदों के साथ (5) भी जोड़ें।
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यदि \(a_1=3\) और \(a_{n+1}=5a_n-2\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=5a_n-2\), what is \(a_3\)?
#recursive-rule
#multiply-minus
#class-9
#hard
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A (59)
B (61)
C (63)
D (65)
Explanation opens after your attempt
Step 1
Concept
\(a_2=5\times3-2=13\) and \(a_3=5\times13-2=63\). Exam tip: subtract (2) after multiplication.
Step 2
Why this answer is correct
The correct answer is C. (63). \(a_2=5\times3-2=13\) and \(a_3=5\times13-2=63\). Exam tip: subtract (2) after multiplication.
Step 3
Exam Tip
\(a_2=5\times3-2=13\) और \(a_3=5\times13-2=63\) है। गुणा के बाद (2) घटाएँ।
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अनुक्रम \(2,5,14,37,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?
Which recursive rule is correct for the sequence \(2,5,14,37,\ldots\)?
#recursive-rule
#identify-rule
#class-9
#hard
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A \(a_1=2, a_{n+1}=2a_n+n^2\)
B \(a_1=2, a_{n+1}=2a_n+n\)
C \(a_1=5, a_{n+1}=2a_n+n^2\)
D \(a_1=2, a_{n+1}=3a_n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_1=2, a_{n+1}=2a_n+n^2\)
Step 1
Concept
\(2\times2+1^2=5\) and \(2\times5+2^2=14\). Exam tip: check the first two steps when choosing a rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_1=2, a_{n+1}=2a_n+n^2\). \(2\times2+1^2=5\) and \(2\times5+2^2=14\). Exam tip: check the first two steps when choosing a rule.
Step 3
Exam Tip
\(2\times2+1^2=5\) और \(2\times5+2^2=14\) मिलता है। नियम चुनते समय शुरुआती दो चरण जाँचें।
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अनुक्रम \(6,9,14,21,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?
Which recursive rule is correct for the sequence \(6,9,14,21,\ldots\)?
#recursive-rule
#identify-rule
#class-9
#hard
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A \(a_1=6, a_{n+1}=a_n+2n\)
B \(a_1=6, a_{n+1}=a_n+2n+1\)
C \(a_1=9, a_{n+1}=a_n+2n+1\)
D \(a_1=6, a_{n+1}=2a_n-3\)
Explanation opens after your attempt
Correct Answer
B. \(a_1=6, a_{n+1}=a_n+2n+1\)
Step 1
Concept
The additions are (3,5,7), so the rule is \(a_{n+1}=a_n+2n+1\). Exam tip: check both first term and changing addition.
Step 2
Why this answer is correct
The correct answer is B. \(a_1=6, a_{n+1}=a_n+2n+1\). The additions are (3,5,7), so the rule is \(a_{n+1}=a_n+2n+1\). Exam tip: check both first term and changing addition.
Step 3
Exam Tip
यहाँ जोड़ (3,5,7) हैं इसलिए नियम \(a_{n+1}=a_n+2n+1\) है। पहले पद और बदलते जोड़ दोनों देखें।
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यदि \(a_1=3\) और \(a_{n+1}=n a_n+2n\) है तो \(a_4\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=n a_n+2n\), what is \(a_4\)?
#recursive-rule
#index-multiplier
#class-9
#hard
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A (42)
B (45)
C (48)
D (51)
Explanation opens after your attempt
Step 1
Concept
\(a_2=5\), \(a_3=14\), and \(a_4=48\). Exam tip: multiply by (n) and add (2n) at each step.
Step 2
Why this answer is correct
The correct answer is C. (48). \(a_2=5\), \(a_3=14\), and \(a_4=48\). Exam tip: multiply by (n) and add (2n) at each step.
Step 3
Exam Tip
\(a_2=5\), \(a_3=14\) और \(a_4=48\) है। हर चरण में (n) से गुणा और (2n) जोड़ना है।
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यदि \(a_1=2\) और (a_{n+1}=(n+1)a_n-1) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and (a_{n+1}=(n+1)a_n-1), what is \(a_4\)?
#recursive-rule
#index-multiplier
#class-9
#hard
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A (27)
B (29)
C (31)
D (33)
Explanation opens after your attempt
Step 1
Concept
\(a_2=3\), \(a_3=8\), and \(a_4=31\). Exam tip: the multiplier (n+1) changes at each step.
Step 2
Why this answer is correct
The correct answer is C. (31). \(a_2=3\), \(a_3=8\), and \(a_4=31\). Exam tip: the multiplier (n+1) changes at each step.
Step 3
Exam Tip
\(a_2=3\), \(a_3=8\) और \(a_4=31\) है। गुणक (n+1) हर चरण में बदलता है।
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यदि \(a_1=200\) और (a_{n+1}=a_n-\(2^n+n^2\)) है तो \(a_4\) क्या होगा?
If \(a_1=200\) and (a_{n+1}=a_n-\(2^n+n^2\)), what is \(a_4\)?
#recursive-rule
#power-plus-square
#class-9
#hard
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A (166)
B (169)
C (172)
D (175)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (3,8,17), so \(a_4=172\). Exam tip: calculate both the power and square before subtracting.
Step 2
Why this answer is correct
The correct answer is C. (172). The subtracted values are (3,8,17), so \(a_4=172\). Exam tip: calculate both the power and square before subtracting.
Step 3
Exam Tip
घटने वाले मान (3,8,17) हैं इसलिए \(a_4=172\) है। घात और वर्ग दोनों निकालकर घटाएँ।
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यदि \(a_1=1\) और \(a_{n+1}=a_n+3^n+n\) है तो \(a_4\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=a_n+3^n+n\), what is \(a_4\)?
#recursive-rule
#power-plus-index
#class-9
#hard
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A (40)
B (43)
C (46)
D (49)
Explanation opens after your attempt
Step 1
Concept
The added values are (4,11,30), so \(a_4=46\). Exam tip: add both \(3^n\) and (n).
Step 2
Why this answer is correct
The correct answer is C. (46). The added values are (4,11,30), so \(a_4=46\). Exam tip: add both \(3^n\) and (n).
Step 3
Exam Tip
जुड़ने वाले मान (4,11,30) हैं इसलिए \(a_4=46\) है। \(3^n\) और (n) दोनों जोड़ें।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=2a_{n-1}+3a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=2a_{n-1}+3a_{n-2}\), what is \(a_4\)?
#recursive-rule
#two-term-recurrence
#class-9
#hard
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A (27)
B (30)
C (33)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times3+3\times2=12\) and \(a_4=2\times12+3\times3=33\). Exam tip: apply coefficients to the correct terms.
Step 2
Why this answer is correct
The correct answer is C. (33). \(a_3=2\times3+3\times2=12\) and \(a_4=2\times12+3\times3=33\). Exam tip: apply coefficients to the correct terms.
Step 3
Exam Tip
\(a_3=2\times3+3\times2=12\) और \(a_4=2\times12+3\times3=33\) है। गुणांकों को सही पदों पर लगाएँ।
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यदि \(a_1=1\), \(a_2=5\) और \(a_n=2a_{n-1}-a_{n-2}+2\) है तो \(a_5\) क्या होगा?
If \(a_1=1\), \(a_2=5\), and \(a_n=2a_{n-1}-a_{n-2}+2\), what is \(a_5\)?
#recursive-rule
#second-order
#class-9
#hard
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A (23)
B (26)
C (29)
D (32)
Explanation opens after your attempt
Step 1
Concept
The terms are (1,5,11,19,29), so \(a_5=29\). Exam tip: subtract in the two-term rule and then add (2).
Step 2
Why this answer is correct
The correct answer is C. (29). The terms are (1,5,11,19,29), so \(a_5=29\). Exam tip: subtract in the two-term rule and then add (2).
Step 3
Exam Tip
पद (1,5,11,19,29) हैं इसलिए \(a_5=29\) है। दो-पद नियम में घटाव के बाद (2) जोड़ें।
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यदि \(a_1=4\) और (a_{n+1}=a_n+\frac{n(n+3)}{2}) है तो \(a_5\) क्या होगा?
If \(a_1=4\) and (a_{n+1}=a_n+\frac{n(n+3)}{2}), what is \(a_5\)?
#recursive-rule
#fractional-increment
#class-9
#hard
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A (30)
B (32)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
The added values are (2,5,9,14), so \(a_5=34\). Exam tip: simplify the fractional increment first.
Step 2
Why this answer is correct
The correct answer is C. (34). The added values are (2,5,9,14), so \(a_5=34\). Exam tip: simplify the fractional increment first.
Step 3
Exam Tip
जुड़ने वाले मान (2,5,9,14) हैं इसलिए \(a_5=34\) है। भिन्न वाले जोड़ को पहले सरल करें।
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यदि \(a_1=90\) और (a_{n+1}=a_n-\frac{n(n+3)}{2}) है तो \(a_4\) क्या होगा?
If \(a_1=90\) and (a_{n+1}=a_n-\frac{n(n+3)}{2}), what is \(a_4\)?
#recursive-rule
#fractional-decrement
#class-9
#hard
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A (70)
B (72)
C (74)
D (76)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (2,5,9), so \(a_4=74\). Exam tip: simplify the fraction before subtracting.
Step 2
Why this answer is correct
The correct answer is C. (74). The subtracted values are (2,5,9), so \(a_4=74\). Exam tip: simplify the fraction before subtracting.
Step 3
Exam Tip
घटने वाले मान (2,5,9) हैं इसलिए \(a_4=74\) है। भिन्न को सरल करके घटाएँ।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+\frac{a_n}{2}+n\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+\frac{a_n}{2}+n\), what is \(a_3\)?
#recursive-rule
#fractional-growth
#class-9
#hard
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A (15)
B (17)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
\(a_2=6+3+1=10\) and \(a_3=10+5+2=17\). Exam tip: take half of the previous term and add (n).
Step 2
Why this answer is correct
The correct answer is B. (17). \(a_2=6+3+1=10\) and \(a_3=10+5+2=17\). Exam tip: take half of the previous term and add (n).
Step 3
Exam Tip
\(a_2=6+3+1=10\) और \(a_3=10+5+2=17\) है। पिछले पद का आधा लेकर (n) जोड़ें।
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यदि \(a_1=4\) और \(a_{n+1}=a_n+\frac{a_n}{4}+n\) है तो \(a_3\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n+\frac{a_n}{4}+n\), what is \(a_3\)?
#recursive-rule
#fractional-growth
#class-9
#hard
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A \(\frac{17}{2}\)
B \(\frac{19}{2}\)
C \(\frac{21}{2}\)
D \(\frac{23}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{19}{2}\)
Step 1
Concept
\(a_2=4+1+1=6\) and \(a_3=6+\frac{6}{4}+2=\frac{19}{2}\). Exam tip: keep fractions exact until the end.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{19}{2}\). \(a_2=4+1+1=6\) and \(a_3=6+\frac{6}{4}+2=\frac{19}{2}\). Exam tip: keep fractions exact until the end.
Step 3
Exam Tip
\(a_2=4+1+1=6\) और \(a_3=6+\frac{6}{4}+2=\frac{19}{2}\) है। भिन्नों को अंत तक ठीक रखें।
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यदि \(a_1=2\) और \(a_{n+1}=a_n^2+n\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=a_n^2+n\), what is \(a_3\)?
#recursive-rule
#nonlinear-recurrence
#class-9
#hard
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A (23)
B (25)
C (27)
D (29)
Explanation opens after your attempt
Step 1
Concept
\(a_2=2^2+1=5\) and \(a_3=5^2+2=27\). Exam tip: square the previous term and add the current (n).
Step 2
Why this answer is correct
The correct answer is C. (27). \(a_2=2^2+1=5\) and \(a_3=5^2+2=27\). Exam tip: square the previous term and add the current (n).
Step 3
Exam Tip
\(a_2=2^2+1=5\) और \(a_3=5^2+2=27\) है। पिछले पद का वर्ग लेकर वर्तमान (n) जोड़ें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n^2-n\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n^2-n\), what is \(a_3\)?
#recursive-rule
#nonlinear-recurrence
#class-9
#hard
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A (58)
B (60)
C (62)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(a_2=3^2-1=8\) and \(a_3=8^2-2=62\). Exam tip: square first and then subtract (n).
Step 2
Why this answer is correct
The correct answer is C. (62). \(a_2=3^2-1=8\) and \(a_3=8^2-2=62\). Exam tip: square first and then subtract (n).
Step 3
Exam Tip
\(a_2=3^2-1=8\) और \(a_3=8^2-2=62\) है। वर्ग निकालकर (n) घटाएँ।
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यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+2a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_4\)?
#recursive-rule
#two-term-plus-index
#class-9
#hard
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A (16)
B (18)
C (20)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3+2\times2+3=10\) and \(a_4=10+2\times3+4=20\). Exam tip: do not forget to add the current (n).
Step 2
Why this answer is correct
The correct answer is C. (20). \(a_3=3+2\times2+3=10\) and \(a_4=10+2\times3+4=20\). Exam tip: do not forget to add the current (n).
Step 3
Exam Tip
\(a_3=3+2\times2+3=10\) और \(a_4=10+2\times3+4=20\) है। वर्तमान (n) भी जोड़ना न भूलें।
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यदि \(a_1=3\), \(a_2=4\) और \(a_n=3a_{n-1}-a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=3\), \(a_2=4\), and \(a_n=3a_{n-1}-a_{n-2}+n\), what is \(a_4\)?
#recursive-rule
#second-order
#class-9
#hard
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A (32)
B (34)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
\(a_3=3\times4-3+3=12\) and \(a_4=3\times12-4+4=36\). Exam tip: use both previous terms and current (n).
Step 2
Why this answer is correct
The correct answer is C. (36). \(a_3=3\times4-3+3=12\) and \(a_4=3\times12-4+4=36\). Exam tip: use both previous terms and current (n).
Step 3
Exam Tip
\(a_3=3\times4-3+3=12\) और \(a_4=3\times12-4+4=36\) है। दोनों पिछले पदों और वर्तमान (n) का उपयोग करें।
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यदि \(a_1=5\) और (a_{n+1}=2a_n+(-1)^n) है तो \(a_4\) क्या होगा?
If \(a_1=5\) and (a_{n+1}=2a_n+(-1)^n), what is \(a_4\)?
#recursive-rule
#alternating-sign
#class-9
#hard
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A (33)
B (35)
C (37)
D (39)
Explanation opens after your attempt
Step 1
Concept
The terms are (5,9,19,37), so \(a_4=37\). Exam tip: check the sign of ((-1)^n) at each step.
Step 2
Why this answer is correct
The correct answer is C. (37). The terms are (5,9,19,37), so \(a_4=37\). Exam tip: check the sign of ((-1)^n) at each step.
Step 3
Exam Tip
पद (5,9,19,37) हैं इसलिए \(a_4=37\) है। ((-1)^n) का चिह्न हर चरण में जाँचें।
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यदि \(a_1=30\) और (a_{n+1}=a_n-(-1)^n(2n+1)) है तो \(a_4\) क्या होगा?
If \(a_1=30\) and (a_{n+1}=a_n-(-1)^n(2n+1)), what is \(a_4\)?
#recursive-rule
#alternating-sign
#class-9
#hard
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? Hint Small clue
A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
The terms are (30,33,28,35), so \(a_4=35\). Exam tip: track the minus sign and ((-1)^n) together.
Step 2
Why this answer is correct
The correct answer is C. (35). The terms are (30,33,28,35), so \(a_4=35\). Exam tip: track the minus sign and ((-1)^n) together.
Step 3
Exam Tip
पद (30,33,28,35) हैं इसलिए \(a_4=35\) है। ऋण चिह्न और ((-1)^n) को साथ में देखें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n+n!\) है तो \(a_5\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n+n!\), what is \(a_5\)?
#recursive-rule
#factorial-increment
#class-9
#hard
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? Hint Small clue
A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
The added values (1!,2!,3!,4!) are (1,2,6,24), so \(a_5=36\). Exam tip: add factorial values in order.
Step 2
Why this answer is correct
The correct answer is B. (36). The added values (1!,2!,3!,4!) are (1,2,6,24), so \(a_5=36\). Exam tip: add factorial values in order.
Step 3
Exam Tip
जुड़ने वाले मान (1!,2!,3!,4!) अर्थात (1,2,6,24) हैं इसलिए \(a_5=36\) है। फैक्टोरियल मान क्रम से जोड़ें।
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यदि \(a_1=100\) और \(a_{n+1}=a_n-n!\) है तो \(a_5\) क्या होगा?
If \(a_1=100\) and \(a_{n+1}=a_n-n!\), what is \(a_5\)?
#recursive-rule
#factorial-decrement
#class-9
#hard
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A (63)
B (65)
C (67)
D (69)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (1,2,6,24), so \(a_5=67\). Exam tip: write factorial subtractions in order.
Step 2
Why this answer is correct
The correct answer is C. (67). The subtracted values are (1,2,6,24), so \(a_5=67\). Exam tip: write factorial subtractions in order.
Step 3
Exam Tip
घटने वाले मान (1,2,6,24) हैं इसलिए \(a_5=67\) है। फैक्टोरियल घटावों को क्रम से लिखें।
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यदि \(a_1=1\) और \(a_{n+1}=2a_n+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=1\) and \(a_{n+1}=2a_n+n^2\), what is \(a_4\)?
#recursive-rule
#double-plus-square
#class-9
#hard
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A (25)
B (27)
C (29)
D (31)
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,10,29), so \(a_4=29\). Exam tip: double first and then add \(n^2\).
Step 2
Why this answer is correct
The correct answer is C. (29). The terms are (1,3,10,29), so \(a_4=29\). Exam tip: double first and then add \(n^2\).
Step 3
Exam Tip
पद (1,3,10,29) हैं इसलिए \(a_4=29\) है। पहले दोगुना करें फिर \(n^2\) जोड़ें।
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यदि \(a_1=2\) और \(a_{n+1}=3a_n+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=3a_n+n^2\), what is \(a_3\)?
#recursive-rule
#triple-plus-square
#class-9
#hard
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A (21)
B (23)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
\(a_2=3\times2+1=7\) and \(a_3=3\times7+4=25\). Exam tip: do both multiplication and square addition.
Step 2
Why this answer is correct
The correct answer is C. (25). \(a_2=3\times2+1=7\) and \(a_3=3\times7+4=25\). Exam tip: do both multiplication and square addition.
Step 3
Exam Tip
\(a_2=3\times2+1=7\) और \(a_3=3\times7+4=25\) है। गुणा और वर्ग जोड़ दोनों करें।
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अनुक्रम \(4,13,40,121,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?
Which recursive rule is correct for the sequence \(4,13,40,121,\ldots\)?
#recursive-rule
#identify-rule
#class-9
#hard
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A \(a_1=4, a_{n+1}=2a_n+5\)
B \(a_1=4, a_{n+1}=3a_n-1\)
C \(a_1=4, a_{n+1}=3a_n+1\)
D \(a_1=13, a_{n+1}=3a_n+1\)
Explanation opens after your attempt
Correct Answer
C. \(a_1=4, a_{n+1}=3a_n+1\)
Step 1
Concept
\(3\times4+1=13\) and \(3\times13+1=40\). Exam tip: both the first term and rule must match.
Step 2
Why this answer is correct
The correct answer is C. \(a_1=4, a_{n+1}=3a_n+1\). \(3\times4+1=13\) and \(3\times13+1=40\). Exam tip: both the first term and rule must match.
Step 3
Exam Tip
\(3\times4+1=13\) और \(3\times13+1=40\) है। पहला पद और नियम दोनों मिलाने चाहिए।
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अनुक्रम \(9,7,10,6,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?
Which recursive rule is correct for the sequence \(9,7,10,6,\ldots\)?
#recursive-rule
#identify-rule
#alternating
#class-9
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A (a_1=9, a_{n+1}=a_n+(-1)^n(n+1))
B \(a_1=9, a_{n+1}=a_n+n+1\)
C (a_1=7, a_{n+1}=a_n+(-1)^n(n+1))
D \(a_1=9, a_{n+1}=a_n-2n\)
Explanation opens after your attempt
Correct Answer
A. (a_1=9, a_{n+1}=a_n+(-1)^n(n+1))
Step 1
Concept
For (n=1), (-2) is added; for (n=2), (+3); and for (n=3), (-4). This alternating rule is correct.
Step 2
Why this answer is correct
The correct answer is A. (a_1=9, a_{n+1}=a_n+(-1)^n(n+1)). For (n=1), (-2) is added; for (n=2), (+3); and for (n=3), (-4). This alternating rule is correct.
Step 3
Exam Tip
(n=1) पर (-2), (n=2) पर (+3) और (n=3) पर (-4) जुड़ता है। यही वैकल्पिक नियम सही है।
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यदि \(a_1=8\) और \(a_{n+1}=\frac{a_n}{2}+a_1\) है तो \(a_4\) क्या होगा?
If \(a_1=8\) and \(a_{n+1}=\frac{a_n}{2}+a_1\), what is \(a_4\)?
#recursive-rule
#first-term-and-half
#class-9
#hard
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A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
The terms are (8,12,14,15), so \(a_4=15\). Exam tip: \(a_1\) stays fixed and half of the previous term is used.
Step 2
Why this answer is correct
The correct answer is C. (15). The terms are (8,12,14,15), so \(a_4=15\). Exam tip: \(a_1\) stays fixed and half of the previous term is used.
Step 3
Exam Tip
पद (8,12,14,15) हैं इसलिए \(a_4=15\) है। \(a_1\) स्थिर रहता है और पिछले पद का आधा लिया जाता है।
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यदि \(a_1=7\) और \(a_{n+1}=a_n+na_1\) है तो \(a_4\) क्या होगा?
If \(a_1=7\) and \(a_{n+1}=a_n+na_1\), what is \(a_4\)?
#recursive-rule
#first-term-and-index
#class-9
#hard
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A (42)
B (45)
C (49)
D (56)
Explanation opens after your attempt
Step 1
Concept
The terms are (7,14,28,49), so \(a_4=49\). Exam tip: \(a_1\) is fixed while (n) changes.
Step 2
Why this answer is correct
The correct answer is C. (49). The terms are (7,14,28,49), so \(a_4=49\). Exam tip: \(a_1\) is fixed while (n) changes.
Step 3
Exam Tip
पद (7,14,28,49) हैं इसलिए \(a_4=49\) है। \(a_1\) स्थिर है और (n) बदलता है।
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यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}+a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=5\), and \(a_n=2a_{n-1}+a_{n-2}+n\), what is \(a_4\)?
#recursive-rule
#two-term-plus-index
#class-9
#hard
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A (35)
B (37)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times5+2+3=15\) and \(a_4=2\times15+5+4=39\). Exam tip: add the current (n) also in a two-term rule.
Step 2
Why this answer is correct
The correct answer is C. (39). \(a_3=2\times5+2+3=15\) and \(a_4=2\times15+5+4=39\). Exam tip: add the current (n) also in a two-term rule.
Step 3
Exam Tip
\(a_3=2\times5+2+3=15\) और \(a_4=2\times15+5+4=39\) है। दो-पद नियम में वर्तमान (n) भी जोड़ें।
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यदि \(a_1=100\) और (a_{n+1}=a_n-\(2^n+n^2+n\)) है तो \(a_4\) क्या होगा?
If \(a_1=100\) and (a_{n+1}=a_n-\(2^n+n^2+n\)), what is \(a_4\)?
#recursive-rule
#power-square-index
#class-9
#hard
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A (58)
B (62)
C (64)
D (66)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (4,10,20), so \(a_4=100-34=66\). Exam tip: add the power, square, and (n) before subtracting.
Step 2
Why this answer is correct
The correct answer is D. (66). The subtracted values are (4,10,20), so \(a_4=100-34=66\). Exam tip: add the power, square, and (n) before subtracting.
Step 3
Exam Tip
घटने वाले मान (4,10,20) हैं इसलिए \(a_4=100-34=66\) है। घात, वर्ग और (n) तीनों को पहले जोड़ें।
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