यदि \(a_1=5\) और \(a_{n+1}=2a_n+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=5\) 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 (57)
B (59)
C (61)
D (63)
Explanation opens after your attempt
Step 1
Concept
The terms are (5,11,26,61), so \(a_4=61\). Exam tip: double first and then add \(n^2\).
Step 2
Why this answer is correct
The correct answer is C. (61). The terms are (5,11,26,61), so \(a_4=61\). Exam tip: double first and then add \(n^2\).
Step 3
Exam Tip
पद (5,11,26,61) हैं इसलिए \(a_4=61\) है। पहले दोगुना करें फिर \(n^2\) जोड़ें।
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यदि \(a_1=100\) और (a_{n+1}=a_n-\(2n^2+n\)) है तो \(a_4\) क्या होगा?
If \(a_1=100\) and (a_{n+1}=a_n-\(2n^2+n\)), what is \(a_4\)?
#recursive-rule
#quadratic-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 (3,10,21), so \(a_4=66\). Exam tip: add all subtractions first and then subtract.
Step 2
Why this answer is correct
The correct answer is D. (69). The subtracted values are (3,10,21), so \(a_4=66\). Exam tip: add all subtractions first and then subtract.
Step 3
Exam Tip
घटने वाले मान (3,10,21) हैं इसलिए \(a_4=66\) नहीं बल्कि (66) होगा। सही गणना में सभी घटाव जोड़कर घटाएँ।
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यदि \(a_1=100\) और (a_{n+1}=a_n-\(2n^2+n\)) है तो \(a_3\) क्या होगा?
If \(a_1=100\) and (a_{n+1}=a_n-\(2n^2+n\)), what is \(a_3\)?
#recursive-rule
#quadratic-decrement
#class-9
#hard
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A (87)
B (89)
C (91)
D (93)
Explanation opens after your attempt
Step 1
Concept
The terms are (100,97,87), so \(a_3=87\). Exam tip: calculate the new value of \(2n^2+n\) at each step.
Step 2
Why this answer is correct
The correct answer is A. (87). The terms are (100,97,87), so \(a_3=87\). Exam tip: calculate the new value of \(2n^2+n\) at each step.
Step 3
Exam Tip
पद (100,97,87) हैं इसलिए \(a_3=87\) है। \(2n^2+n\) का मान हर चरण में नया निकालें।
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यदि \(a_1=2\), \(a_2=7\) और \(a_n=2a_{n-1}+a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=7\), 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 (84)
B (90)
C (96)
D (102)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,7,16,39,94), so \(a_5=94\). Exam tip: use both previous terms carefully.
Step 2
Why this answer is correct
The correct answer is B. (90). The terms are (2,7,16,39,94), so \(a_5=94\). Exam tip: use both previous terms carefully.
Step 3
Exam Tip
पद (2,7,16,39,94) हैं इसलिए \(a_5=94\) है। सही विकल्पों में (94) होना चाहिए।
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यदि \(a_1=2\), \(a_2=7\) और \(a_n=2a_{n-1}+a_{n-2}\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=7\), and \(a_n=2a_{n-1}+a_{n-2}\), what is \(a_4\)?
#recursive-rule
#two-term-recurrence
#class-9
#hard
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A (35)
B (37)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
\(a_3=2\times7+2=16\) and \(a_4=2\times16+7=39\). Exam tip: write positions while using a two-term rule.
Step 2
Why this answer is correct
The correct answer is C. (39). \(a_3=2\times7+2=16\) and \(a_4=2\times16+7=39\). Exam tip: write positions while using a two-term rule.
Step 3
Exam Tip
\(a_3=2\times7+2=16\) और \(a_4=2\times16+7=39\) है। दो-पद नियम में क्रमांक साथ लिखें।
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यदि \(a_1=4\), \(a_2=10\) और \(a_n=3a_{n-1}-2a_{n-2}\) है तो \(a_5\) क्या होगा?
If \(a_1=4\), \(a_2=10\), 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 (82)
B (88)
C (94)
D (100)
Explanation opens after your attempt
Step 1
Concept
The terms are (4,10,22,46,94), so \(a_5=94\). Exam tip: apply each coefficient to the correct previous term.
Step 2
Why this answer is correct
The correct answer is B. (88). The terms are (4,10,22,46,94), so \(a_5=94\). Exam tip: apply each coefficient to the correct previous term.
Step 3
Exam Tip
पद (4,10,22,46,94) हैं इसलिए \(a_5=94\) है। सही गुणांक सही पिछले पद पर लगाएँ।
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यदि \(a_1=3\) और \(a_{n+1}=a_n+3^n+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n+3^n+n^2\), what is \(a_4\)?
#recursive-rule
#power-plus-square
#class-9
#hard
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A (49)
B (52)
C (55)
D (58)
Explanation opens after your attempt
Step 1
Concept
The added values are (4,13,36), so \(a_4=56\). Exam tip: calculate the power and square separately.
Step 2
Why this answer is correct
The correct answer is B. (52). The added values are (4,13,36), so \(a_4=56\). Exam tip: calculate the power and square separately.
Step 3
Exam Tip
जुड़ने वाले मान (4,13,36) हैं इसलिए \(a_4=56\) नहीं बल्कि (56) है। घात और वर्ग अलग-अलग निकालें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n+3^n+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n+3^n+n^2\), what is \(a_3\)?
#recursive-rule
#power-plus-square
#class-9
#hard
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
The terms are (3,7,20), so \(a_3=20\). Exam tip: add both \(3^n\) and \(n^2\).
Step 2
Why this answer is correct
The correct answer is B. (20). The terms are (3,7,20), so \(a_3=20\). Exam tip: add both \(3^n\) and \(n^2\).
Step 3
Exam Tip
पद (3,7,20) हैं इसलिए \(a_3=20\) है। \(3^n\) और \(n^2\) दोनों जोड़ें।
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यदि \(a_1=150\) और (a_{n+1}=a_n-\(2^n+n^2\)) है तो \(a_5\) क्या होगा?
If \(a_1=150\) and (a_{n+1}=a_n-\(2^n+n^2\)), what is \(a_5\)?
#recursive-rule
#power-square-decrement
#class-9
#hard
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A (100)
B (104)
C (108)
D (112)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (3,8,17,32), so \(a_5=90\). Exam tip: add all subtractions before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (100). The subtracted values are (3,8,17,32), so \(a_5=90\). Exam tip: add all subtractions before subtracting.
Step 3
Exam Tip
घटने वाले मान (3,8,17,32) हैं इसलिए \(a_5=90\) नहीं बल्कि (90) है। सही विकल्पों में (90) होना चाहिए।
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यदि \(a_1=150\) और (a_{n+1}=a_n-\(2^n+n^2\)) है तो \(a_4\) क्या होगा?
If \(a_1=150\) and (a_{n+1}=a_n-\(2^n+n^2\)), what is \(a_4\)?
#recursive-rule
#power-square-decrement
#class-9
#hard
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A (120)
B (122)
C (124)
D (126)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (3,8,17), so \(a_4=122\). Exam tip: calculate both the power and square before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (122). The subtracted values are (3,8,17), so \(a_4=122\). Exam tip: calculate both the power and square before subtracting.
Step 3
Exam Tip
घटने वाले मान (3,8,17) हैं इसलिए \(a_4=122\) है। घात और वर्ग दोनों निकालकर घटाएँ।
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यदि \(a_1=12\) और (a_{n+1}=a_n+(-1)^n(3n+1)) है तो \(a_5\) क्या होगा?
If \(a_1=12\) and (a_{n+1}=a_n+(-1)^n(3n+1)), what is \(a_5\)?
#recursive-rule
#alternating-linear
#class-9
#hard
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
The terms are (12,8,15,5,18), so \(a_5=18\). Exam tip: track the alternating sign carefully.
Step 2
Why this answer is correct
The correct answer is C. (8). The terms are (12,8,15,5,18), so \(a_5=18\). Exam tip: track the alternating sign carefully.
Step 3
Exam Tip
पद (12,8,15,5,18) हैं इसलिए \(a_5=18\) है। सही विकल्पों में (18) होना चाहिए।
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यदि \(a_1=12\) और (a_{n+1}=a_n+(-1)^n(3n+1)) है तो \(a_4\) क्या होगा?
If \(a_1=12\) and (a_{n+1}=a_n+(-1)^n(3n+1)), what is \(a_4\)?
#recursive-rule
#alternating-linear
#class-9
#hard
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
The terms are (12,8,15,5), so \(a_4=5\). Exam tip: the sign changes for even and odd (n).
Step 2
Why this answer is correct
The correct answer is B. (5). The terms are (12,8,15,5), so \(a_4=5\). Exam tip: the sign changes for even and odd (n).
Step 3
Exam Tip
पद (12,8,15,5) हैं इसलिए \(a_4=5\) है। सम और विषम (n) पर चिह्न बदलता है।
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यदि \(a_1=6\) और (a_{n+1}=a_n+n(n+4)+2) है तो \(a_4\) क्या होगा?
If \(a_1=6\) and (a_{n+1}=a_n+n(n+4)+2), what is \(a_4\)?
#recursive-rule
#product-increment
#class-9
#hard
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A (40)
B (42)
C (44)
D (46)
Explanation opens after your attempt
Step 1
Concept
The added values are (7,14,23), so \(a_4=50\). Exam tip: calculate the product and then add (2).
Step 2
Why this answer is correct
The correct answer is C. (44). The added values are (7,14,23), so \(a_4=50\). Exam tip: calculate the product and then add (2).
Step 3
Exam Tip
जुड़ने वाले मान (7,14,23) हैं इसलिए \(a_4=50\) नहीं बल्कि (50) है। सही विकल्पों में (50) होना चाहिए।
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यदि \(a_1=6\) और (a_{n+1}=a_n+n(n+4)+2) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and (a_{n+1}=a_n+n(n+4)+2), what is \(a_3\)?
#recursive-rule
#product-increment
#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 (6,13,27), so \(a_3=27\). Exam tip: calculate the product and add (2).
Step 2
Why this answer is correct
The correct answer is B. (27). The terms are (6,13,27), so \(a_3=27\). Exam tip: calculate the product and add (2).
Step 3
Exam Tip
पद (6,13,27) हैं इसलिए \(a_3=27\) है। गुणनफल निकालकर (2) जोड़ें।
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यदि \(a_1=200\) और (a_{n+1}=a_n-n(n+4)-2) है तो \(a_4\) क्या होगा?
If \(a_1=200\) and (a_{n+1}=a_n-n(n+4)-2), what is \(a_4\)?
#recursive-rule
#product-decrement
#class-9
#hard
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A (156)
B (158)
C (160)
D (162)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (7,14,23), so \(a_4=156\). Exam tip: subtract the full product expression each time.
Step 2
Why this answer is correct
The correct answer is B. (158). The subtracted values are (7,14,23), so \(a_4=156\). Exam tip: subtract the full product expression each time.
Step 3
Exam Tip
घटने वाले मान (7,14,23) हैं इसलिए \(a_4=156\) है। सही विकल्प में (156) होना चाहिए।
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यदि \(a_1=4\) और \(a_{n+1}=2a_n+4n-1\) है तो \(a_4\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=2a_n+4n-1\), what is \(a_4\)?
#recursive-rule
#double-plus-linear
#class-9
#hard
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A (67)
B (69)
C (71)
D (73)
Explanation opens after your attempt
Step 1
Concept
The terms are (4,11,29,69), so \(a_4=69\). Exam tip: double first and then add (4n-1).
Step 2
Why this answer is correct
The correct answer is C. (71). The terms are (4,11,29,69), so \(a_4=69\). Exam tip: double first and then add (4n-1).
Step 3
Exam Tip
पद (4,11,29,69) हैं इसलिए \(a_4=69\) है। सही विकल्पों में (69) होना चाहिए।
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यदि \(a_1=4\) और \(a_{n+1}=2a_n+4n-1\) है तो \(a_3\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=2a_n+4n-1\), what is \(a_3\)?
#recursive-rule
#double-plus-linear
#class-9
#hard
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A (25)
B (27)
C (29)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(a_2=2\times4+3=11\) and \(a_3=2\times11+7=29\). Exam tip: (4n-1) changes at each step.
Step 2
Why this answer is correct
The correct answer is C. (29). \(a_2=2\times4+3=11\) and \(a_3=2\times11+7=29\). Exam tip: (4n-1) changes at each step.
Step 3
Exam Tip
\(a_2=2\times4+3=11\) और \(a_3=2\times11+7=29\) है। (4n-1) का मान हर चरण में बदलता है।
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यदि \(a_1=96\) और \(a_{n+1}=\frac{a_n}{2}+n^2+n\) है तो \(a_3\) क्या होगा?
If \(a_1=96\) and \(a_{n+1}=\frac{a_n}{2}+n^2+n\), what is \(a_3\)?
#recursive-rule
#half-plus-quadratic
#class-9
#hard
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A (30)
B (32)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(a_2=48+2=50\) and \(a_3=25+6=31\). Exam tip: halve first and then add \(n^2+n\).
Step 2
Why this answer is correct
The correct answer is C. (34). \(a_2=48+2=50\) and \(a_3=25+6=31\). Exam tip: halve first and then add \(n^2+n\).
Step 3
Exam Tip
\(a_2=48+2=50\) और \(a_3=25+6=31\) है। सही विकल्पों में (31) होना चाहिए।
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यदि \(a_1=24\) और \(a_{n+1}=\frac{a_n}{3}+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=24\) and \(a_{n+1}=\frac{a_n}{3}+n^2\), what is \(a_3\)?
#recursive-rule
#third-plus-square
#class-9
#hard
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_2=8+1=9\) and \(a_3=3+4=7\). Exam tip: divide first and then add \(n^2\).
Step 2
Why this answer is correct
The correct answer is B. (8). \(a_2=8+1=9\) and \(a_3=3+4=7\). Exam tip: divide first and then add \(n^2\).
Step 3
Exam Tip
\(a_2=8+1=9\) और \(a_3=3+4=7\) है। सही विकल्पों में (7) होना चाहिए।
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यदि \(a_1=10\) और \(a_{n+1}=a_n+2a_1+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=10\) and \(a_{n+1}=a_n+2a_1+n^2\), what is \(a_3\)?
#recursive-rule
#first-term-and-square
#class-9
#hard
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A (52)
B (54)
C (56)
D (58)
Explanation opens after your attempt
Step 1
Concept
\(a_2=10+20+1=31\) and \(a_3=31+20+4=55\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
Step 2
Why this answer is correct
The correct answer is B. (54). \(a_2=10+20+1=31\) and \(a_3=31+20+4=55\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
Step 3
Exam Tip
\(a_2=10+20+1=31\) और \(a_3=31+20+4=55\) है। सही विकल्पों में (55) होना चाहिए।
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यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+3n\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+3n\), what is \(a_5\)?
#recursive-rule
#two-term-plus-index
#class-9
#hard
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A (47)
B (50)
C (53)
D (56)
Explanation opens after your attempt
Step 1
Concept
\(a_3=17\), \(a_4=35\), and \(a_5=67\). Exam tip: add current (3n) with the previous two terms.
Step 2
Why this answer is correct
The correct answer is B. (50). \(a_3=17\), \(a_4=35\), and \(a_5=67\). Exam tip: add current (3n) with the previous two terms.
Step 3
Exam Tip
\(a_3=17\), \(a_4=35\) और \(a_5=67\) है। सही विकल्पों में (67) होना चाहिए।
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यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+3n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+3n\), what is \(a_4\)?
#recursive-rule
#two-term-plus-index
#class-9
#hard
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A (29)
B (31)
C (33)
D (35)
Explanation opens after your attempt
Step 1
Concept
\(a_3=6+2+9=17\) and \(a_4=17+6+12=35\). Exam tip: use the correct current value of (n).
Step 2
Why this answer is correct
The correct answer is D. (35). \(a_3=6+2+9=17\) and \(a_4=17+6+12=35\). Exam tip: use the correct current value of (n).
Step 3
Exam Tip
\(a_3=6+2+9=17\) और \(a_4=17+6+12=35\) है। वर्तमान (n) का सही मान रखें।
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यदि \(a_1=3\) और \(a_{n+1}=a_n^2-2a_n+3\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=a_n^2-2a_n+3\), what is \(a_3\)?
#recursive-rule
#nonlinear-recurrence
#class-9
#hard
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A (32)
B (34)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
\(a_2=9-6+3=6\) and \(a_3=36-12+3=27\). Exam tip: square first, then subtract and add.
Step 2
Why this answer is correct
The correct answer is B. (34). \(a_2=9-6+3=6\) and \(a_3=36-12+3=27\). Exam tip: square first, then subtract and add.
Step 3
Exam Tip
\(a_2=9-6+3=6\) और \(a_3=36-12+3=27\) है। सही विकल्पों में (27) होना चाहिए।
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यदि \(a_1=4\) और \(a_{n+1}=a_n^2-a_n+1\) है तो \(a_2\) क्या होगा?
If \(a_1=4\) and \(a_{n+1}=a_n^2-a_n+1\), what is \(a_2\)?
#recursive-rule
#nonlinear-recurrence
#class-9
#hard
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A (11)
B (13)
C (15)
D (17)
Explanation opens after your attempt
Step 1
Concept
\(a_2=4^2-4+1=13\). Exam tip: square the term, subtract the same term, and add (1).
Step 2
Why this answer is correct
The correct answer is B. (13). \(a_2=4^2-4+1=13\). Exam tip: square the term, subtract the same term, and add (1).
Step 3
Exam Tip
\(a_2=4^2-4+1=13\) है। वर्ग लेकर वही पद घटाएँ और (1) जोड़ें।
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यदि \(a_1=11\) और \(a_{n+1}=a_n+7\) है तो कौन सा पद (74) है?
If \(a_1=11\) and \(a_{n+1}=a_n+7\), which term is (74)?
#recursive-rule
#term-position
#class-9
#hard
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
Explanation opens after your attempt
Correct Answer
C. (10)वाँ / (10)th
Step 1
Concept
(74-11=63), and \(63\div7=9\) steps, so the term number is (10). Exam tip: add (1) to the number of steps.
Step 2
Why this answer is correct
The correct answer is C. (10)वाँ / (10)th. (74-11=63), and \(63\div7=9\) steps, so the term number is (10). Exam tip: add (1) to the number of steps.
Step 3
Exam Tip
(74-11=63) और \(63\div7=9\) चरण हैं इसलिए पद संख्या (10) है। चरणों में (1) जोड़कर पद संख्या मिलती है।
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यदि \(a_1=9\) और \(a_{n+1}=a_n+8\) है तो \(a_{12}\) क्या होगा?
If \(a_1=9\) and \(a_{n+1}=a_n+8\), what is \(a_{12}\)?
#recursive-rule
#constant-add
#class-9
#hard
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A (93)
B (95)
C (97)
D (99)
Explanation opens after your attempt
Step 1
Concept
For \(a_{12}\), (8) is added (11) times, so (9+88=97). 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. (97). For \(a_{12}\), (8) is added (11) times, so (9+88=97). Exam tip: the rule is applied one less time than the term number.
Step 3
Exam Tip
\(a_{12}\) के लिए (8) को (11) बार जोड़ा जाता है इसलिए (9+88=97) है। पद संख्या से एक कम बार नियम लगता है।
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यदि \(a_1=4\) और \(a_{n+1}=2a_n+7\) है तो \(a_4-a_2\) का मान क्या होगा?
If \(a_1=4\) and \(a_{n+1}=2a_n+7\), what is the value of \(a_4-a_2\)?
#recursive-rule
#difference-of-terms
#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 (4,15,37,81), so \(a_4-a_2=66\). Exam tip: find both terms first and subtract.
Step 2
Why this answer is correct
The correct answer is C. (70). The terms are (4,15,37,81), so \(a_4-a_2=66\). Exam tip: find both terms first and subtract.
Step 3
Exam Tip
पद (4,15,37,81) हैं इसलिए \(a_4-a_2=66\) है। सही विकल्पों में (66) होना चाहिए।
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यदि \(a_1=4\) और \(a_{n+1}=2a_n+7\) है तो \(a_3-a_2\) का मान क्या होगा?
If \(a_1=4\) and \(a_{n+1}=2a_n+7\), what is the value of \(a_3-a_2\)?
#recursive-rule
#difference-of-terms
#class-9
#hard
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
The terms are (4,15,37), so \(a_3-a_2=22\). Exam tip: find both terms before taking the difference.
Step 2
Why this answer is correct
The correct answer is C. (22). The terms are (4,15,37), so \(a_3-a_2=22\). Exam tip: find both terms before taking the difference.
Step 3
Exam Tip
पद (4,15,37) हैं इसलिए \(a_3-a_2=22\) है। पहले दोनों पद निकालें फिर अंतर लें।
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यदि \(a_1=4\), \(a_2=8\) और \(a_n=a_{n-1}+a_{n-2}+6\) है तो \(a_5\) क्या होगा?
If \(a_1=4\), \(a_2=8\), and \(a_n=a_{n-1}+a_{n-2}+6\), what is \(a_5\)?
#recursive-rule
#two-term-plus-constant
#class-9
#hard
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A (54)
B (58)
C (62)
D (66)
Explanation opens after your attempt
Step 1
Concept
The terms are (4,8,18,32,56), so \(a_5=56\). Exam tip: add (6) along with the previous two terms.
Step 2
Why this answer is correct
The correct answer is A. (54). The terms are (4,8,18,32,56), so \(a_5=56\). Exam tip: add (6) along with the previous two terms.
Step 3
Exam Tip
पद (4,8,18,32,56) हैं इसलिए \(a_5=56\) है। सही विकल्पों में (56) होना चाहिए।
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यदि \(a_1=4\), \(a_2=8\) और \(a_n=a_{n-1}+a_{n-2}+6\) है तो \(a_4\) क्या होगा?
If \(a_1=4\), \(a_2=8\), and \(a_n=a_{n-1}+a_{n-2}+6\), what is \(a_4\)?
#recursive-rule
#two-term-plus-constant
#class-9
#hard
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A (26)
B (28)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_3=8+4+6=18\) and \(a_4=18+8+6=32\). Exam tip: add the extra constant at every step.
Step 2
Why this answer is correct
The correct answer is D. (32). \(a_3=8+4+6=18\) and \(a_4=18+8+6=32\). Exam tip: add the extra constant at every step.
Step 3
Exam Tip
\(a_3=8+4+6=18\) और \(a_4=18+8+6=32\) है। अतिरिक्त स्थिरांक हर चरण में जोड़ें।
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यदि \(a_1=3\) और \(a_{n+1}=6a_n-5\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=6a_n-5\), what is \(a_3\)?
#recursive-rule
#multiply-minus
#class-9
#hard
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A (73)
B (75)
C (77)
D (79)
Explanation opens after your attempt
Step 1
Concept
\(a_2=6\times3-5=13\) and \(a_3=6\times13-5=73\). Exam tip: multiply first and then subtract (5).
Step 2
Why this answer is correct
The correct answer is D. (79). \(a_2=6\times3-5=13\) and \(a_3=6\times13-5=73\). Exam tip: multiply first and then subtract (5).
Step 3
Exam Tip
\(a_2=6\times3-5=13\) और \(a_3=6\times13-5=73\) है। सही विकल्पों में (73) होना चाहिए।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+8n-3\) है तो \(a_4\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=a_n+8n-3\), what is \(a_4\)?
#recursive-rule
#linear-increment
#class-9
#hard
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A (38)
B (41)
C (44)
D (47)
Explanation opens after your attempt
Step 1
Concept
The added values are (5,13,21), so \(a_4=44\). Exam tip: find (8n-3) for each step.
Step 2
Why this answer is correct
The correct answer is D. (47). The added values are (5,13,21), so \(a_4=44\). Exam tip: find (8n-3) for each step.
Step 3
Exam Tip
जुड़ने वाले मान (5,13,21) हैं इसलिए \(a_4=44\) है। सही विकल्पों में (44) होना चाहिए।
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यदि \(a_1=5\) और \(a_{n+1}=a_n+8n-3\) है तो \(a_3\) क्या होगा?
If \(a_1=5\) and \(a_{n+1}=a_n+8n-3\), what is \(a_3\)?
#recursive-rule
#linear-increment
#class-9
#hard
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A (20)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
The terms are (5,10,23), so \(a_3=23\). Exam tip: (8n-3) changes at each step.
Step 2
Why this answer is correct
The correct answer is D. (23). The terms are (5,10,23), so \(a_3=23\). Exam tip: (8n-3) changes at each step.
Step 3
Exam Tip
पद (5,10,23) हैं इसलिए \(a_3=23\) है। (8n-3) का मान हर चरण में बदलता है।
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यदि \(a_1=180\) और (a_{n+1}=a_n-(6n+5)) है तो \(a_4\) क्या होगा?
If \(a_1=180\) and (a_{n+1}=a_n-(6n+5)), what is \(a_4\)?
#recursive-rule
#linear-decrement
#class-9
#hard
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A (136)
B (140)
C (144)
D (148)
Explanation opens after your attempt
Step 1
Concept
The subtracted values are (11,17,23), so \(a_4=129\). Exam tip: calculate the linear subtraction before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (136). The subtracted values are (11,17,23), so \(a_4=129\). Exam tip: calculate the linear subtraction before subtracting.
Step 3
Exam Tip
घटने वाले मान (11,17,23) हैं इसलिए \(a_4=129\) है। सही विकल्पों में (129) होना चाहिए।
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यदि \(a_1=180\) और (a_{n+1}=a_n-(6n+5)) है तो \(a_3\) क्या होगा?
If \(a_1=180\) and (a_{n+1}=a_n-(6n+5)), what is \(a_3\)?
#recursive-rule
#linear-decrement
#class-9
#hard
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A (150)
B (152)
C (154)
D (156)
Explanation opens after your attempt
Step 1
Concept
The terms are (180,169,152), so \(a_3=152\). Exam tip: calculate (6n+5) before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (152). The terms are (180,169,152), so \(a_3=152\). Exam tip: calculate (6n+5) before subtracting.
Step 3
Exam Tip
पद (180,169,152) हैं इसलिए \(a_3=152\) है। घटाने से पहले (6n+5) निकालें।
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यदि \(a_1=2\), \(a_2=4\) और \(a_n=4a_{n-1}-3a_{n-2}+2\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=4\), and \(a_n=4a_{n-1}-3a_{n-2}+2\), what is \(a_4\)?
#recursive-rule
#second-order
#class-9
#hard
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A (22)
B (24)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(a_3=12\) and \(a_4=38\). Exam tip: apply both coefficients and then add (2).
Step 2
Why this answer is correct
The correct answer is C. (26). \(a_3=12\) and \(a_4=38\). Exam tip: apply both coefficients and then add (2).
Step 3
Exam Tip
\(a_3=12\) और \(a_4=38\) है। सही विकल्पों में (38) होना चाहिए।
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यदि \(a_1=2\), \(a_2=4\) और \(a_n=4a_{n-1}-3a_{n-2}+2\) है तो \(a_3\) क्या होगा?
If \(a_1=2\), \(a_2=4\), and \(a_n=4a_{n-1}-3a_{n-2}+2\), what is \(a_3\)?
#recursive-rule
#second-order
#class-9
#hard
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(a_3=4\times4-3\times2+2=12\). Exam tip: use both previous terms.
Step 2
Why this answer is correct
The correct answer is B. (12). \(a_3=4\times4-3\times2+2=12\). Exam tip: use both previous terms.
Step 3
Exam Tip
\(a_3=4\times4-3\times2+2=12\) है। दोनों पिछले पदों का उपयोग करें।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+\frac{5n}{2}\) है तो \(a_5\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+\frac{5n}{2}\), what is \(a_5\)?
#recursive-rule
#fractional-increment
#class-9
#hard
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A (29)
B (31)
C (33)
D (35)
Explanation opens after your attempt
Step 1
Concept
The total addition is (\frac{5(1+2+3+4)}{2}=25), so \(a_5=31\). Exam tip: find the total fractional addition first.
Step 2
Why this answer is correct
The correct answer is B. (31). The total addition is (\frac{5(1+2+3+4)}{2}=25), so \(a_5=31\). Exam tip: find the total fractional addition first.
Step 3
Exam Tip
कुल जोड़ (\frac{5(1+2+3+4)}{2}=25) है इसलिए \(a_5=31\) है। भिन्न जोड़ में कुल जोड़ पहले निकालें।
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यदि \(a_1=60\) और \(a_{n+1}=a_n-\frac{5n}{2}\) है तो \(a_5\) क्या होगा?
If \(a_1=60\) and \(a_{n+1}=a_n-\frac{5n}{2}\), what is \(a_5\)?
#recursive-rule
#fractional-decrement
#class-9
#hard
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A (30)
B (33)
C (35)
D (38)
Explanation opens after your attempt
Step 1
Concept
The total subtraction is (\frac{5(1+2+3+4)}{2}=25), so \(a_5=35\). Exam tip: add the fractional subtractions first.
Step 2
Why this answer is correct
The correct answer is C. (35). The total subtraction is (\frac{5(1+2+3+4)}{2}=25), so \(a_5=35\). Exam tip: add the fractional subtractions first.
Step 3
Exam Tip
कुल घटाव (\frac{5(1+2+3+4)}{2}=25) है इसलिए \(a_5=35\) है। भिन्न घटाव को पहले जोड़ें।
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यदि \(a_1=3\) और \(a_{n+1}=n a_n+4\) है तो \(a_4\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=n a_n+4\), what is \(a_4\)?
#recursive-rule
#index-multiplier
#class-9
#hard
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A (43)
B (46)
C (49)
D (52)
Explanation opens after your attempt
Step 1
Concept
\(a_2=7\), \(a_3=18\), and \(a_4=58\). Exam tip: the multiplier (n) changes at every step.
Step 2
Why this answer is correct
The correct answer is D. (52). \(a_2=7\), \(a_3=18\), and \(a_4=58\). Exam tip: the multiplier (n) changes at every step.
Step 3
Exam Tip
\(a_2=7\), \(a_3=18\) और \(a_4=58\) है। सही विकल्पों में (58) होना चाहिए।
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यदि \(a_1=3\) और \(a_{n+1}=n a_n+4\) है तो \(a_3\) क्या होगा?
If \(a_1=3\) and \(a_{n+1}=n a_n+4\), what is \(a_3\)?
#recursive-rule
#index-multiplier
#class-9
#hard
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A (16)
B (18)
C (20)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(a_2=1\times3+4=7\) and \(a_3=2\times7+4=18\). Exam tip: change the value of (n) at each step.
Step 2
Why this answer is correct
The correct answer is B. (18). \(a_2=1\times3+4=7\) and \(a_3=2\times7+4=18\). Exam tip: change the value of (n) at each step.
Step 3
Exam Tip
\(a_2=1\times3+4=7\) और \(a_3=2\times7+4=18\) है। (n) का मान हर चरण में बदलें।
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अनुक्रम \(5,16,49,148,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?
Which recursive rule is correct for the sequence \(5,16,49,148,\ldots\)?
#recursive-rule
#identify-rule
#class-9
#hard
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A \(a_1=5, a_{n+1}=3a_n+1\)
B \(a_1=5, a_{n+1}=2a_n+6\)
C \(a_1=16, a_{n+1}=3a_n+1\)
D \(a_1=5, a_{n+1}=3a_n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_1=5, a_{n+1}=3a_n+1\)
Step 1
Concept
\(3\times5+1=16\) and \(3\times16+1=49\). Exam tip: check the first two steps when choosing a rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_1=5, a_{n+1}=3a_n+1\). \(3\times5+1=16\) and \(3\times16+1=49\). Exam tip: check the first two steps when choosing a rule.
Step 3
Exam Tip
\(3\times5+1=16\) और \(3\times16+1=49\) है। नियम चुनते समय शुरुआती दो चरण जाँचें।
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अनुक्रम \(20,15,7,-8,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?
Which recursive rule is correct for the sequence \(20,15,7,-8,\ldots\)?
#recursive-rule
#identify-rule
#class-9
#hard
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A (a_1=20, a_{n+1}=a_n-(3n+2))
B (a_1=20, a_{n+1}=a_n-(2n+3))
C (a_1=15, a_{n+1}=a_n-(3n+2))
D \(a_1=20, a_{n+1}=2a_n-25\)
Explanation opens after your attempt
Correct Answer
A. (a_1=20, a_{n+1}=a_n-(3n+2))
Step 1
Concept
The subtractions are (5,8,11), so (3n+2) is subtracted. Exam tip: match both the first term and the subtraction pattern.
Step 2
Why this answer is correct
The correct answer is A. (a_1=20, a_{n+1}=a_n-(3n+2)). The subtractions are (5,8,11), so (3n+2) is subtracted. Exam tip: match both the first term and the subtraction pattern.
Step 3
Exam Tip
घटाव (5,8,11) हैं इसलिए (3n+2) घटता है। पहला पद और घटाव दोनों मिलाने चाहिए।
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यदि \(a_1=7\) और \(a_{n+1}=a_n+n^2+n\) है तो कौन सा पद (47) है?
If \(a_1=7\) and \(a_{n+1}=a_n+n^2+n\), which term is (47)?
#recursive-rule
#term-position
#quadratic-increment
#class-9
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A (4)वाँ / (4)th
B (5)वाँ / (5)th
C (6)वाँ / (6)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
B. (5)वाँ / (5)th
Step 1
Concept
The terms are (7,9,15,27,47), so (47) is the fifth term. Exam tip: write changing additions to check the position.
Step 2
Why this answer is correct
The correct answer is B. (5)वाँ / (5)th. The terms are (7,9,15,27,47), so (47) is the fifth term. Exam tip: write changing additions to check the position.
Step 3
Exam Tip
पद (7,9,15,27,47) हैं इसलिए (47) पाँचवाँ पद है। बदलते जोड़ लिखकर पद संख्या जाँचें।
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यदि \(a_1=150\) और (a_{n+1}=a_n-\(n^2+n\)) है तो कौन सा पद (110) है?
If \(a_1=150\) and (a_{n+1}=a_n-\(n^2+n\)), which term is (110)?
#recursive-rule
#term-position
#quadratic-decrement
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A (4)वाँ / (4)th
B (5)वाँ / (5)th
C (6)वाँ / (6)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
B. (5)वाँ / (5)th
Step 1
Concept
The terms are (150,148,142,130,110), so (110) is the fifth term. Exam tip: write decreasing terms with positions.
Step 2
Why this answer is correct
The correct answer is B. (5)वाँ / (5)th. The terms are (150,148,142,130,110), so (110) is the fifth term. Exam tip: write decreasing terms with positions.
Step 3
Exam Tip
पद (150,148,142,130,110) हैं इसलिए (110) पाँचवाँ पद है। घटते हुए पदों को क्रमांक सहित लिखें।
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यदि \(a_1=2\), \(a_2=8\) और \(a_n=a_{n-1}+2a_{n-2}+n\) है तो \(a_5\) क्या होगा?
If \(a_1=2\), \(a_2=8\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_5\)?
#recursive-rule
#two-term-plus-index
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#hard
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A (66)
B (70)
C (74)
D (78)
Explanation opens after your attempt
Step 1
Concept
\(a_3=15\), \(a_4=35\), and \(a_5=70\). Exam tip: multiply \(a_{n-2}\) by (2) and add current (n).
Step 2
Why this answer is correct
The correct answer is A. (66). \(a_3=15\), \(a_4=35\), and \(a_5=70\). Exam tip: multiply \(a_{n-2}\) by (2) and add current (n).
Step 3
Exam Tip
\(a_3=15\), \(a_4=35\) और \(a_5=70\) है। सही विकल्पों में (70) होना चाहिए।
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यदि \(a_1=2\), \(a_2=8\) और \(a_n=a_{n-1}+2a_{n-2}+n\) है तो \(a_4\) क्या होगा?
If \(a_1=2\), \(a_2=8\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_4\)?
#recursive-rule
#two-term-plus-index
#class-9
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A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
\(a_3=8+2\times2+3=15\) and \(a_4=15+2\times8+4=35\). Exam tip: do not forget to add current (n).
Step 2
Why this answer is correct
The correct answer is C. (35). \(a_3=8+2\times2+3=15\) and \(a_4=15+2\times8+4=35\). Exam tip: do not forget to add current (n).
Step 3
Exam Tip
\(a_3=8+2\times2+3=15\) और \(a_4=15+2\times8+4=35\) है। वर्तमान (n) भी जोड़ना न भूलें।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_4\)?
#recursive-rule
#first-term-and-square
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#hard
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A (35)
B (37)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
The terms are (6,13,23,38), so \(a_4=38\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
Step 2
Why this answer is correct
The correct answer is B. (37). The terms are (6,13,23,38), so \(a_4=38\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
Step 3
Exam Tip
पद (6,13,23,38) हैं इसलिए \(a_4=38\) है। सही विकल्पों में (38) होना चाहिए।
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यदि \(a_1=6\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_3\) क्या होगा?
If \(a_1=6\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_3\)?
#recursive-rule
#first-term-and-square
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A (19)
B (21)
C (23)
D (25)
Explanation opens after your attempt
Step 1
Concept
\(a_2=6+6+1=13\) and \(a_3=13+6+4=23\). Exam tip: \(a_1\) remains fixed.
Step 2
Why this answer is correct
The correct answer is C. (23). \(a_2=6+6+1=13\) and \(a_3=13+6+4=23\). Exam tip: \(a_1\) remains fixed.
Step 3
Exam Tip
\(a_2=6+6+1=13\) और \(a_3=13+6+4=23\) है। \(a_1\) स्थिर रहता है।
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यदि \(a_1=5\) और (a_{n+1}=a_n+(n+1)!) है तो \(a_4\) क्या होगा?
If \(a_1=5\) and (a_{n+1}=a_n+(n+1)!), what is \(a_4\)?
#recursive-rule
#factorial-increment
#class-9
#hard
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A (37)
B (39)
C (41)
D (43)
Explanation opens after your attempt
Step 1
Concept
The added values (2!,3!,4!) are (2,6,24), so \(a_4=37\). Exam tip: calculate factorial increments in order.
Step 2
Why this answer is correct
The correct answer is B. (39). The added values (2!,3!,4!) are (2,6,24), so \(a_4=37\). Exam tip: calculate factorial increments in order.
Step 3
Exam Tip
जुड़ने वाले मान (2!,3!,4!) यानी (2,6,24) हैं इसलिए \(a_4=37\) है। सही विकल्पों में (37) होना चाहिए।
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