अनुक्रम \(3,8,15,24,\ldots\) में (n)वाँ पद \(a_n=n^2+2n\) है। दसवाँ पद क्या होगा?
In the sequence \(3,8,15,24,\ldots\), the (n)th term is \(a_n=n^2+2n\). What is the tenth term?
#sequences
#nth-term
#class-9
#hard
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A (100)
B (110)
C (120)
D (130)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=10^2+2\times10=120\), so the correct answer is (120). Exam tip: substitute the given position directly for (n).
Step 2
Why this answer is correct
The correct answer is C. (120). \(a_{10}=10^2+2\times10=120\), so the correct answer is (120). Exam tip: substitute the given position directly for (n).
Step 3
Exam Tip
\(a_{10}=10^2+2\times10=120\) इसलिए सही उत्तर (120) है। परीक्षा में (n) की जगह सीधे दिया गया क्रमांक रखें।
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अनुक्रम \(2,6,12,20,\ldots\) का सामान्य पद (a_n=n(n+1)) है। कौन सा पद (72) के बराबर है?
The sequence \(2,6,12,20,\ldots\) has general term (a_n=n(n+1)). Which term is equal to (72)?
#sequences
#term-position
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#hard
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
B. (8)वाँ / (8)th
Step 1
Concept
For (n(n+1)=72), \(8\times9=72\). Exam tip: check nearby factor pairs quickly.
Step 2
Why this answer is correct
The correct answer is B. (8)वाँ / (8)th. For (n(n+1)=72), \(8\times9=72\). Exam tip: check nearby factor pairs quickly.
Step 3
Exam Tip
(n(n+1)=72) में \(8\times9=72\) मिलता है। ऐसी स्थिति में आस-पास के गुणनखंड जल्दी जाँचें।
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अनुक्रम \(1,4,9,16,\ldots\) में (15)वें पद और (14)वें पद का अंतर कितना है?
In the sequence \(1,4,9,16,\ldots\), what is the difference between the (15)th term and the (14)th term?
#sequences
#squares
#difference
#class-9
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A (27)
B (28)
C (29)
D (30)
Explanation opens after your attempt
Step 1
Concept
The difference is (152 -142 =(15-14)(15+14)=29). Exam tip: use the identity \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is C. (29). The difference is (152 -142 =(15-14)(15+14)=29). Exam tip: use the identity \(a^2-b^2\).
Step 3
Exam Tip
वर्गों के अंतर में (152 -142 =(15-14)(15+14)=29) होता है। परीक्षा में \(a^2-b^2\) का सूत्र याद रखें।
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अनुक्रम \(5,11,19,29,41,\ldots\) में अगला पद क्या होगा?
What is the next term in the sequence \(5,11,19,29,41,\ldots\)?
#sequences
#differences
#next-term
#class-9
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A (53)
B (54)
C (55)
D (56)
Explanation opens after your attempt
Step 1
Concept
The differences are (6,8,10,12), so the next difference is (14). Thus (41+14=55).
Step 2
Why this answer is correct
The correct answer is C. (55). The differences are (6,8,10,12), so the next difference is (14). Thus (41+14=55).
Step 3
Exam Tip
अंतर (6,8,10,12) हैं इसलिए अगला अंतर (14) होगा। (41+14=55) मिलता है।
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अनुक्रम \(4,9,18,31,48,\ldots\) में पदों के अंतर \(5,9,13,17,\ldots\) हैं। अगला पद क्या है?
In the sequence \(4,9,18,31,48,\ldots\), the differences are \(5,9,13,17,\ldots\). What is the next term?
#sequences
#second-difference
#class-9
#hard
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A (65)
B (69)
C (70)
D (73)
Explanation opens after your attempt
Step 1
Concept
The differences increase by (4), so the next difference is (21). Therefore (48+21=69).
Step 2
Why this answer is correct
The correct answer is B. (69). The differences increase by (4), so the next difference is (21). Therefore (48+21=69).
Step 3
Exam Tip
अंतर (4) से बढ़ रहे हैं इसलिए अगला अंतर (21) होगा। (48+21=69) सही है।
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अनुक्रम \(2,5,10,17,26,\ldots\) का (n)वाँ पद \(a_n=n^2+1\) है। \(a_{12}-a_{10}\) का मान क्या है?
For the sequence \(2,5,10,17,26,\ldots\), the (n)th term is \(a_n=n^2+1\). What is the value of \(a_{12}-a_{10}\)?
#sequences
#nth-term
#difference
#class-9
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A (40)
B (42)
C (44)
D (46)
Explanation opens after your attempt
Step 1
Concept
\(a_{12}=145\) and \(a_{10}=101\), so the difference is (44). Exam tip: find both terms separately first.
Step 2
Why this answer is correct
The correct answer is C. (44). \(a_{12}=145\) and \(a_{10}=101\), so the difference is (44). Exam tip: find both terms separately first.
Step 3
Exam Tip
\(a_{12}=145\) और \(a_{10}=101\) इसलिए अंतर (44) है। पहले दोनों पद अलग-अलग निकालें।
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अनुक्रम \(7,14,23,34,47,\ldots\) में पहला अंतर (7) है और हर बार अंतर (2) बढ़ता है। छठा पद क्या होगा?
In the sequence \(7,14,23,34,47,\ldots\), the first difference is (7) and each difference increases by (2). What is the sixth term?
#sequences
#changing-differences
#class-9
#hard
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A (58)
B (60)
C (61)
D (62)
Explanation opens after your attempt
Step 1
Concept
The next difference is (15), so the sixth term is (47+15=62). Exam tip: write changing differences separately.
Step 2
Why this answer is correct
The correct answer is D. (62). The next difference is (15), so the sixth term is (47+15=62). Exam tip: write changing differences separately.
Step 3
Exam Tip
अगला अंतर (15) होगा इसलिए छठा पद (47+15=62) है। बदलते अंतरों को अलग पंक्ति में लिखना उपयोगी रहता है।
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अनुक्रम \(1,3,6,10,15,\ldots\) में कौन सा पद (45) है?
In the sequence \(1,3,6,10,15,\ldots\), which term is (45)?
#sequences
#triangular-numbers
#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
B. (9)वाँ / (9)th
Step 1
Concept
This is a triangular sequence with (T_n=\frac{n(n+1)}{2}). Since \(\frac{9\times10}{2}=45\), it is the (9)th term.
Step 2
Why this answer is correct
The correct answer is B. (9)वाँ / (9)th. This is a triangular sequence with (T_n=\frac{n(n+1)}{2}). Since \(\frac{9\times10}{2}=45\), it is the (9)th term.
Step 3
Exam Tip
यह त्रिभुजीय अनुक्रम है और (T_n=\frac{n(n+1)}{2}) होता है। \(\frac{9\times10}{2}=45\) इसलिए यह (9)वाँ पद है।
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अनुक्रम \(2,4,8,16,\ldots\) में \(a_1=2\) और हर अगला पद पिछले पद का दोगुना है। आठवाँ पद क्या होगा?
In the sequence \(2,4,8,16,\ldots\), \(a_1=2\) and each next term is double the previous term. What is the eighth term?
#sequences
#powers
#next-term
#class-9
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A (128)
B (192)
C (256)
D (512)
Explanation opens after your attempt
Step 1
Concept
The eighth term is \(2^8=256\). Exam tip: identify powers in doubling sequences.
Step 2
Why this answer is correct
The correct answer is C. (256). The eighth term is \(2^8=256\). Exam tip: identify powers in doubling sequences.
Step 3
Exam Tip
आठवाँ पद \(2^8=256\) है। दोगुने वाले अनुक्रम में घातों को पहचानें।
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अनुक्रम \(81,27,9,3,\ldots\) में प्रत्येक पद पिछले पद का \(\frac{1}{3}\) है। छठा पद क्या होगा?
In the sequence \(81,27,9,3,\ldots\), each term is \(\frac{1}{3}\) of the previous term. What is the sixth term?
#sequences
#geometric
#ratio
#class-9
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A (1)
B \(\frac{1}{3}\)
C \(\frac{1}{9}\)
D (0)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3}\)
Step 1
Concept
The terms are \(81,27,9,3,1,\frac{1}{3}\). Exam tip: divide each term by (3) step by step.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). The terms are \(81,27,9,3,1,\frac{1}{3}\). Exam tip: divide each term by (3) step by step.
Step 3
Exam Tip
पद हैं \(81,27,9,3,1,\frac{1}{3}\)। क्रम से घटाते समय हर पद को \(\frac{3}{1}\) से न बाँटें बल्कि (3) से बाँटें।
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अनुक्रम \(4,7,12,19,28,\ldots\) में \(a_n=n^2+3\) है। कौन सा पद (84) है?
In the sequence \(4,7,12,19,28,\ldots\), \(a_n=n^2+3\). Which term is (84)?
#sequences
#nth-term
#perfect-square
#class-9
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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
B. (9)वाँ / (9)th
Step 1
Concept
From \(n^2+3=84\), \(n^2=81\) and (n=9). Exam tip: recognizing perfect squares saves time.
Step 2
Why this answer is correct
The correct answer is B. (9)वाँ / (9)th. From \(n^2+3=84\), \(n^2=81\) and (n=9). Exam tip: recognizing perfect squares saves time.
Step 3
Exam Tip
\(n^2+3=84\) से \(n^2=81\) और (n=9) मिलता है। वर्ग संख्या पहचानना समय बचाता है।
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अनुक्रम \(6,13,24,39,58,\ldots\) में अगला पद ज्ञात कीजिए।
Find the next term in the sequence \(6,13,24,39,58,\ldots\).
#sequences
#differences
#next-term
#class-9
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A (77)
B (79)
C (80)
D (81)
Explanation opens after your attempt
Step 1
Concept
The differences are (7,11,15,19), so the next difference is (23). Thus (58+23=81).
Step 2
Why this answer is correct
The correct answer is D. (81). The differences are (7,11,15,19), so the next difference is (23). Thus (58+23=81).
Step 3
Exam Tip
अंतर (7,11,15,19) हैं इसलिए अगला अंतर (23) होगा। (58+23=81) मिलता है।
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अनुक्रम \(1,8,27,64,\ldots\) में (n)वाँ पद \(n^3\) है। (6)वाँ पद और (5)वाँ पद का अंतर क्या है?
In the sequence \(1,8,27,64,\ldots\), the (n)th term is \(n^3\). What is the difference between the (6)th term and the (5)th term?
#sequences
#cubes
#difference
#class-9
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A (91)
B (81)
C (71)
D (61)
Explanation opens after your attempt
Step 1
Concept
\(6^3-5^3=216-125=91\). Exam tip: in cube sequences, calculate the two cubes and subtract.
Step 2
Why this answer is correct
The correct answer is A. (91). \(6^3-5^3=216-125=91\). Exam tip: in cube sequences, calculate the two cubes and subtract.
Step 3
Exam Tip
\(6^3-5^3=216-125=91\) है। घन अनुक्रम में सीधे घन निकालकर घटाएँ।
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अनुक्रम \(10,8,11,9,12,10,\ldots\) में दो उप-अनुक्रम छिपे हैं। अगला पद क्या होगा?
In the sequence \(10,8,11,9,12,10,\ldots\), two subsequences are hidden. What is the next term?
#sequences
#alternating-pattern
#class-9
#hard
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A (11)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
Odd positions are \(10,11,12,\ldots\), so the next odd-position term is (13). Exam tip: separate positions in alternating sequences.
Step 2
Why this answer is correct
The correct answer is B. (13). Odd positions are \(10,11,12,\ldots\), so the next odd-position term is (13). Exam tip: separate positions in alternating sequences.
Step 3
Exam Tip
विषम स्थानों पर \(10,11,12,\ldots\) है इसलिए अगला विषम स्थान (13) होगा। वैकल्पिक अनुक्रम में स्थानों को अलग करें।
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अनुक्रम \(2,9,4,16,6,25,\ldots\) में अगला पद क्या है?
What is the next term in the sequence \(2,9,4,16,6,25,\ldots\)?
#sequences
#alternating
#pattern
#class-9
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A (8)
B (36)
C (49)
D (10)
Explanation opens after your attempt
Step 1
Concept
Odd positions are \(2,4,6,\ldots\), so the next odd-position term is (8). Exam tip: split the two patterns in alternating sequences.
Step 2
Why this answer is correct
The correct answer is A. (8). Odd positions are \(2,4,6,\ldots\), so the next odd-position term is (8). Exam tip: split the two patterns in alternating sequences.
Step 3
Exam Tip
विषम स्थानों पर \(2,4,6,\ldots\) हैं इसलिए अगला विषम पद (8) है। वैकल्पिक पैटर्न में दोनों धाराएँ अलग देखें।
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अनुक्रम \(3,6,11,18,27,\ldots\) में \(a_n=n^2+2\) है। \(a_9\) का मान क्या है?
In the sequence \(3,6,11,18,27,\ldots\), \(a_n=n^2+2\). What is \(a_9\)?
#sequences
#nth-term
#class-9
#hard
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A (79)
B (81)
C (83)
D (85)
Explanation opens after your attempt
Step 1
Concept
\(a_9=9^2+2=83\). Exam tip: when the general term is given, avoid guessing.
Step 2
Why this answer is correct
The correct answer is C. (83). \(a_9=9^2+2=83\). Exam tip: when the general term is given, avoid guessing.
Step 3
Exam Tip
\(a_9=9^2+2=83\) है। सामान्य पद मिलने पर अनुमान नहीं लगाना चाहिए।
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अनुक्रम \(12,17,22,27,\ldots\) में कितने पद (60) से छोटे हैं?
How many terms of the sequence \(12,17,22,27,\ldots\) are less than (60)?
#sequences
#counting-terms
#class-9
#hard
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A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Here (a_n=12+5(n-1)), and (12+5(n-1)<60) gives (n<10.6). So (10) terms are less than (60).
Step 2
Why this answer is correct
The correct answer is C. (10). Here (a_n=12+5(n-1)), and (12+5(n-1)<60) gives (n<10.6). So (10) terms are less than (60).
Step 3
Exam Tip
यहाँ (a_n=12+5(n-1)) और (12+5(n-1)<60) से (n<10.6) मिलता है। इसलिए (10) पद छोटे हैं।
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अनुक्रम \(100,93,86,79,\ldots\) में पहला धनात्मक पदों की संख्या कितनी है?
In the sequence \(100,93,86,79,\ldots\), how many positive terms are there?
#sequences
#arithmetic
#counting
#class-9
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A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
(a_n=100-7(n-1)>0) gives (n<15.28). Therefore the number of positive terms is (15).
Step 2
Why this answer is correct
The correct answer is C. (15). (a_n=100-7(n-1)>0) gives (n<15.28). Therefore the number of positive terms is (15).
Step 3
Exam Tip
(a_n=100-7(n-1)>0) से (n<15.28) मिलता है। अतः धनात्मक पदों की संख्या (15) है।
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अनुक्रम \(5,10,20,40,\ldots\) में कौन सा पद (320) है?
In the sequence \(5,10,20,40,\ldots\), which term is (320)?
#sequences
#geometric
#term-position
#class-9
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A (5)वाँ / (5)th
B (6)वाँ / (6)th
C (7)वाँ / (7)th
D (8)वाँ / (8)th
Explanation opens after your attempt
Correct Answer
C. (7)वाँ / (7)th
Step 1
Concept
The terms are \(5\times2^{n-1}\), and \(5\times2^6=320\). Hence it is the (7)th term.
Step 2
Why this answer is correct
The correct answer is C. (7)वाँ / (7)th. The terms are \(5\times2^{n-1}\), and \(5\times2^6=320\). Hence it is the (7)th term.
Step 3
Exam Tip
पद \(5\times2^{n-1}\) हैं और \(5\times2^6=320\) है। इसलिए यह (7)वाँ पद है।
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अनुक्रम \(2,3,5,8,13,\ldots\) में हर पद पिछले दो पदों का योग है। आठवाँ पद क्या होगा?
In the sequence \(2,3,5,8,13,\ldots\), each term is the sum of the previous two terms. What is the eighth term?
#sequences
#recursive
#fibonacci-type
#class-9
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A (21)
B (34)
C (55)
D (89)
Explanation opens after your attempt
Step 1
Concept
The next terms are (21,34), so the eighth term is (34). Exam tip: do not skip steps in recursive sequences.
Step 2
Why this answer is correct
The correct answer is B. (34). The next terms are (21,34), so the eighth term is (34). Exam tip: do not skip steps in recursive sequences.
Step 3
Exam Tip
आगे के पद (21,34) हैं इसलिए आठवाँ पद (34) है। पुनरावर्ती अनुक्रम में पद छोड़ना नहीं चाहिए।
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अनुक्रम \(4,6,10,16,26,\ldots\) में हर पद पिछले दो पदों का योग है। सातवाँ पद क्या होगा?
In the sequence \(4,6,10,16,26,\ldots\), each term is the sum of the previous two terms. What is the seventh term?
#sequences
#recursive
#position-counting
#class-9
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A (36)
B (40)
C (42)
D (46)
Explanation opens after your attempt
Step 1
Concept
The sixth term is (16+26=42) and the seventh is (26+42=68). Exam tip: count positions carefully in recursive sequences.
Step 2
Why this answer is correct
The correct answer is C. (42). The sixth term is (16+26=42) and the seventh is (26+42=68). Exam tip: count positions carefully in recursive sequences.
Step 3
Exam Tip
छठा पद (16+26=42) और सातवाँ पद (26+42=68) नहीं है क्योंकि पाँचवाँ (26) है। ध्यान से गिनने पर छठा (42) और सातवाँ (68) होगा।
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अनुक्रम \(1,4,10,19,31,\ldots\) में क्रमागत अंतरों में \(3,6,9,12,\ldots\) मिलते हैं। छठा पद क्या है?
In the sequence \(1,4,10,19,31,\ldots\), the successive differences are \(3,6,9,12,\ldots\). What is the sixth term?
#sequences
#difference-pattern
#class-9
#hard
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A (43)
B (45)
C (46)
D (49)
Explanation opens after your attempt
Step 1
Concept
The next difference is (15), so the sixth term is (31+15=46). Exam tip: identifying the sequence of differences is the key step.
Step 2
Why this answer is correct
The correct answer is C. (46). The next difference is (15), so the sixth term is (31+15=46). Exam tip: identifying the sequence of differences is the key step.
Step 3
Exam Tip
अगला अंतर (15) है इसलिए छठा पद (31+15=46) होगा। अंतरों के अनुक्रम को पहचानना मुख्य कदम है।
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अनुक्रम \(50,45,37,26,12,\ldots\) में अंतरों का क्रम \(-5,-8,-11,-14,\ldots\) है। अगला पद क्या होगा?
In the sequence \(50,45,37,26,12,\ldots\), the differences are \(-5,-8,-11,-14,\ldots\). What is the next term?
#sequences
#negative-differences
#next-term
#class-9
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A (0)
B (-3)
C (-5)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The next difference is (-17), so (12-17=-5). Exam tip: be careful with signs in negative differences.
Step 2
Why this answer is correct
The correct answer is C. (-5). The next difference is (-17), so (12-17=-5). Exam tip: be careful with signs in negative differences.
Step 3
Exam Tip
अगला अंतर (-17) होगा इसलिए (12-17=-5) है। ऋणात्मक अंतरों में संकेत का विशेष ध्यान रखें।
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अनुक्रम \(2,7,14,23,34,\ldots\) में \(a_n=n^2+n\) नहीं है। सही सामान्य पद कौन सा है?
In the sequence \(2,7,14,23,34,\ldots\), \(a_n=n^2+n\) is not correct. Which general term is correct?
#sequences
#general-term
#option-testing
#class-9
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A \(a_n=n^2+1\)
B \(a_n=n^2+n\)
C \(a_n=n^2+2n-1\)
D \(a_n=2n^2\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=n^2+2n-1\)
Step 1
Concept
Substituting (n=1,2,3) in \(n^2+2n-1\) gives (2,7,14). Exam tip: test options using the first three terms.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=n^2+2n-1\). Substituting (n=1,2,3) in \(n^2+2n-1\) gives (2,7,14). Exam tip: test options using the first three terms.
Step 3
Exam Tip
(n=1,2,3) रखने पर \(n^2+2n-1\) से (2,7,14) मिलते हैं। विकल्प जाँचते समय शुरुआती तीन पदों परखें।
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अनुक्रम \(0,3,8,15,24,\ldots\) का सामान्य पद कौन सा है?
What is the general term of the sequence \(0,3,8,15,24,\ldots\)?
#sequences
#general-term
#squares
#class-9
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A \(a_n=n^2-1\)
B \(a_n=n^2+1\)
C \(a_n=2n-2\)
D \(a_n=n^2+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-1\)
Step 1
Concept
The terms are \(1^2-1,2^2-1,3^2-1,\ldots\). Exam tip: quickly recognize sequences near perfect squares.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-1\). The terms are \(1^2-1,2^2-1,3^2-1,\ldots\). Exam tip: quickly recognize sequences near perfect squares.
Step 3
Exam Tip
यह पद \(1^2-1,2^2-1,3^2-1,\ldots\) के रूप में हैं। वर्गों के पास वाले अनुक्रम को तुरंत पहचानें।
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अनुक्रम \(3,7,13,21,31,\ldots\) के लिए कौन सा सूत्र सही है?
Which formula is correct for the sequence \(3,7,13,21,31,\ldots\)?
#sequences
#general-term
#quadratic
#class-9
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A \(a_n=n^2+2\)
B \(a_n=n^2+n+1\)
C \(a_n=2n^2-1\)
D \(a_n=3n+1\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+n+1\)
Step 1
Concept
\(n^2+n+1\) gives (3,7,13,21). Exam tip: match the first four terms before choosing a formula.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+n+1\). \(n^2+n+1\) gives (3,7,13,21). Exam tip: match the first four terms before choosing a formula.
Step 3
Exam Tip
\(n^2+n+1\) से (3,7,13,21) मिलते हैं। सूत्र चुनते समय पहले चार पदों से मिलान करें।
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अनुक्रम \(11,18,27,38,51,\ldots\) में अगला पद क्या है?
What is the next term in the sequence \(11,18,27,38,51,\ldots\)?
#sequences
#odd-differences
#next-term
#class-9
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A (62)
B (64)
C (66)
D (68)
Explanation opens after your attempt
Step 1
Concept
The differences are (7,9,11,13), so the next difference is (15). Therefore (51+15=66).
Step 2
Why this answer is correct
The correct answer is C. (66). The differences are (7,9,11,13), so the next difference is (15). Therefore (51+15=66).
Step 3
Exam Tip
अंतर (7,9,11,13) हैं इसलिए अगला अंतर (15) होगा। (51+15=66) सही है।
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अनुक्रम \(2,12,30,56,90,\ldots\) का सही सामान्य पद कौन सा है?
What is the correct general term for the sequence \(2,12,30,56,90,\ldots\)?
#sequences
#general-term
#critical-thinking
#class-9
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A \(a_n=2n^2\)
B \(a_n=n^3+n\)
C (a_n=n-2 (n+1))
D (a_n=n(n+1)2 )
Explanation opens after your attempt
Correct Answer
D. (a_n=n(n+1)2 )
Step 1
Concept
(n(n+1)2 ) does not give the full sequence, so care is needed. None of the given options matches all terms.
Step 2
Why this answer is correct
The correct answer is D. (a_n=n(n+1)2 ). (n(n+1)2 ) does not give the full sequence, so care is needed. None of the given options matches all terms.
Step 3
Exam Tip
(n(n+1)2 ) से (2,12,36) नहीं मिलता इसलिए सावधानी जरूरी है। दिए गए विकल्पों में कोई भी पूरा मेल नहीं खाता।
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अनुक्रम \(9,16,25,36,\ldots\) में (20)वाँ पद क्या है?
What is the (20)th term of the sequence \(9,16,25,36,\ldots\)?
#sequences
#shifted-squares
#class-9
#hard
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A (361)
B (400)
C (441)
D (484)
Explanation opens after your attempt
Step 1
Concept
This is \(3^2,4^2,5^2,\ldots\), so the (20)th term is \(22^2=484\). Exam tip: track how the index shifts.
Step 2
Why this answer is correct
The correct answer is D. (484). This is \(3^2,4^2,5^2,\ldots\), so the (20)th term is \(22^2=484\). Exam tip: track how the index shifts.
Step 3
Exam Tip
यह \(3^2,4^2,5^2,\ldots\) है इसलिए (20)वाँ पद \(22^2=484\) होगा। शुरुआती संख्या से सूचकांक का संबंध ध्यान रखें।
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अनुक्रम \(8,27,64,125,\ldots\) में (10)वाँ पद क्या है?
What is the (10)th term of the sequence \(8,27,64,125,\ldots\)?
#sequences
#shifted-cubes
#nth-term
#class-9
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A (1000)
B (1331)
C (1728)
D (2197)
Explanation opens after your attempt
Step 1
Concept
This is \(2^3,3^3,4^3,\ldots\), so the (10)th term is \(11^3=1331\). Exam tip: handle shifted cube sequences carefully.
Step 2
Why this answer is correct
The correct answer is B. (1331). This is \(2^3,3^3,4^3,\ldots\), so the (10)th term is \(11^3=1331\). Exam tip: handle shifted cube sequences carefully.
Step 3
Exam Tip
यह \(2^3,3^3,4^3,\ldots\) है इसलिए (10)वाँ पद \(11^3=1331\) है। शिफ्ट वाले घन अनुक्रमों में क्रमांक ध्यान से बदलें।
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अनुक्रम \(1,2,4,7,11,\ldots\) में प्रत्येक बार जोड़ी जाने वाली संख्या \(1,2,3,4,\ldots\) है। आठवाँ पद क्या होगा?
In the sequence \(1,2,4,7,11,\ldots\), the added numbers are \(1,2,3,4,\ldots\). What is the eighth term?
#sequences
#cumulative-sum
#class-9
#hard
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A (20)
B (22)
C (26)
D (29)
Explanation opens after your attempt
Step 1
Concept
Continuing gives (16,22,29), so the eighth term is (29). Exam tip: write each successive addition to avoid mistakes.
Step 2
Why this answer is correct
The correct answer is D. (29). Continuing gives (16,22,29), so the eighth term is (29). Exam tip: write each successive addition to avoid mistakes.
Step 3
Exam Tip
आगे (16,22,29) मिलते हैं इसलिए आठवाँ पद (29) है। क्रमागत जोड़ को पूरा लिखना गलती घटाता है।
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अनुक्रम \(3,5,9,17,33,\ldots\) में हर अगला पद पिछले पद का दोगुना घटाकर (1) है। अगला पद क्या होगा?
In the sequence \(3,5,9,17,33,\ldots\), each next term is double the previous term minus (1). What is the next term?
#sequences
#recurrence
#next-term
#class-9
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A (63)
B (64)
C (65)
D (66)
Explanation opens after your attempt
Step 1
Concept
\(2\times33-1=65\). Exam tip: apply the given recurrence rule exactly.
Step 2
Why this answer is correct
The correct answer is C. (65). \(2\times33-1=65\). Exam tip: apply the given recurrence rule exactly.
Step 3
Exam Tip
\(2\times33-1=65\) है। पुनरावर्ती नियम में पहले दिए गए नियम को ठीक से लागू करें।
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अनुक्रम \(2,5,11,23,47,\ldots\) में हर अगला पद पिछले पद का दोगुना जोड़कर (1) है। अगला पद क्या होगा?
In the sequence \(2,5,11,23,47,\ldots\), each next term is double the previous term plus (1). What is the next term?
#sequences
#recurrence
#pattern
#class-9
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A (93)
B (94)
C (95)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(2\times47+1=95\). Exam tip: do not change the order of multiplication and addition.
Step 2
Why this answer is correct
The correct answer is C. (95). \(2\times47+1=95\). Exam tip: do not change the order of multiplication and addition.
Step 3
Exam Tip
\(2\times47+1=95\) है। ऐसे प्रश्नों में गुणा और जोड़ का क्रम न बदलें।
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अनुक्रम \(30,15,17,8.5,10.5,\ldots\) में क्रम है आधा करना फिर (2) जोड़ना। अगला पद क्या होगा?
In the sequence \(30,15,17,8.5,10.5,\ldots\), the pattern is divide by (2), then add (2). What is the next term?
#sequences
#alternating-operations
#class-9
#hard
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A (4.25)
B (5.25)
C (6.25)
D (12.5)
Explanation opens after your attempt
Step 1
Concept
After (10.5), dividing by (2) gives (5.25). Exam tip: identify the next operation in alternating-operation sequences.
Step 2
Why this answer is correct
The correct answer is B. (5.25). After (10.5), dividing by (2) gives (5.25). Exam tip: identify the next operation in alternating-operation sequences.
Step 3
Exam Tip
(10.5) के बाद आधा करने पर (5.25) मिलता है। वैकल्पिक क्रिया वाले अनुक्रम में अगली क्रिया पहचानें।
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अनुक्रम \(1,4,13,40,121,\ldots\) में हर अगला पद पिछले पद का (3) गुना जोड़कर (1) है। अगला पद क्या होगा?
In the sequence \(1,4,13,40,121,\ldots\), each next term is (3) times the previous term plus (1). What is the next term?
#sequences
#recurrence
#multiply-add
#class-9
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A (362)
B (363)
C (364)
D (365)
Explanation opens after your attempt
Step 1
Concept
\(3\times121+1=364\). Exam tip: apply the given rule to the last term directly.
Step 2
Why this answer is correct
The correct answer is C. (364). \(3\times121+1=364\). Exam tip: apply the given rule to the last term directly.
Step 3
Exam Tip
\(3\times121+1=364\) है। दिए गए नियम को अंतिम पद पर लगाना सबसे सुरक्षित तरीका है।
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अनुक्रम \(7,10,16,28,52,\ldots\) में हर बार जोड़ा गया पद दोगुना हो रहा है। अगला पद क्या होगा?
In the sequence \(7,10,16,28,52,\ldots\), the added amount doubles each time. What is the next term?
#sequences
#doubling-differences
#class-9
#hard
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A (76)
B (88)
C (96)
D (100)
Explanation opens after your attempt
Step 1
Concept
The differences are (3,6,12,24), so the next difference is (48). Thus (52+48=100).
Step 2
Why this answer is correct
The correct answer is D. (100). The differences are (3,6,12,24), so the next difference is (48). Thus (52+48=100).
Step 3
Exam Tip
अंतर (3,6,12,24) हैं इसलिए अगला अंतर (48) होगा। (52+48=100) मिलता है।
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अनुक्रम \(2,4,7,11,16,\ldots\) में (20)वाँ पद क्या होगा?
What is the (20)th term of the sequence \(2,4,7,11,16,\ldots\)?
#sequences
#triangular-shift
#nth-term
#class-9
50 50-50 2 wrong hide
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? Hint Small clue
A (191)
B (192)
C (211)
D (212)
Explanation opens after your attempt
Step 1
Concept
It adds consecutive numbers starting from (1), so (a_n=1+\frac{n(n+1)}{2}). Thus \(a_{20}=1+\frac{20\times21}{2}=211\).
Step 2
Why this answer is correct
The correct answer is C. (211). It adds consecutive numbers starting from (1), so (a_n=1+\frac{n(n+1)}{2}). Thus \(a_{20}=1+\frac{20\times21}{2}=211\).
Step 3
Exam Tip
यह (1) से शुरू होकर क्रमागत संख्याएँ जोड़ता है और (a_n=1+\frac{n(n+1)}{2}) है। \(a_{20}=1+\frac{20\times21}{2}=211\) है।
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अनुक्रम \(13,18,23,28,\ldots\) में कौन सा पद (98) है?
In the sequence \(13,18,23,28,\ldots\), which term is (98)?
#sequences
#arithmetic
#term-position
#class-9
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A (16)वाँ / (16)th
B (17)वाँ / (17)th
C (18)वाँ / (18)th
D (19)वाँ / (19)th
Explanation opens after your attempt
Correct Answer
C. (18)वाँ / (18)th
Step 1
Concept
(a_n=13+5(n-1)), and (13+5(n-1)=98) gives (n=18). Exam tip: do not forget (n-1) when finding position.
Step 2
Why this answer is correct
The correct answer is C. (18)वाँ / (18)th. (a_n=13+5(n-1)), and (13+5(n-1)=98) gives (n=18). Exam tip: do not forget (n-1) when finding position.
Step 3
Exam Tip
(a_n=13+5(n-1)) और (13+5(n-1)=98) से (n=18) मिलता है। पद संख्या निकालते समय (n-1) न भूलें।
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अनुक्रम \(6,13,20,27,\ldots\) का कौन सा पद (83) है?
Which term of the sequence \(6,13,20,27,\ldots\) is (83)?
#sequences
#arithmetic-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
(6+7(n-1)=83) gives (7(n-1)=77) and (n=12). Exam tip: use the arithmetic sequence formula directly.
Step 2
Why this answer is correct
The correct answer is C. (12)वाँ / (12)th. (6+7(n-1)=83) gives (7(n-1)=77) and (n=12). Exam tip: use the arithmetic sequence formula directly.
Step 3
Exam Tip
(6+7(n-1)=83) से (7(n-1)=77) और (n=12) मिलता है। समान अंतर वाले अनुक्रम में सूत्र सीधे लगाएँ।
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अनुक्रम \(-5,-1,3,7,\ldots\) में (25)वाँ पद क्या है?
What is the (25)th term of the sequence \(-5,-1,3,7,\ldots\)?
#sequences
#negative-start
#nth-term
#class-9
50 50-50 2 wrong hide
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? Hint Small clue
A (87)
B (91)
C (95)
D (99)
Explanation opens after your attempt
Step 1
Concept
(a_n=-5+4(n-1)), so \(a_{25}=-5+96=91\). Exam tip: handle the sign of a negative first term carefully.
Step 2
Why this answer is correct
The correct answer is B. (91). (a_n=-5+4(n-1)), so \(a_{25}=-5+96=91\). Exam tip: handle the sign of a negative first term carefully.
Step 3
Exam Tip
(a_n=-5+4(n-1)) है इसलिए \(a_{25}=-5+96=91\) है। ऋणात्मक पहले पद में संकेत सावधानी से रखें।
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अनुक्रम \(1,-2,4,-8,16,\ldots\) में आठवाँ पद क्या होगा?
What will be the eighth term in the sequence \(1,-2,4,-8,16,\ldots\)?
#sequences
#alternating-sign
#geometric
#class-9
50 50-50 2 wrong hide
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? Hint Small clue
A (64)
B (-64)
C (128)
D (-128)
Explanation opens after your attempt
Step 1
Concept
Each term is multiplied by (-2), so the eighth term is ((-2)7 =-128). Exam tip: track both sign and power.
Step 2
Why this answer is correct
The correct answer is D. (-128). Each term is multiplied by (-2), so the eighth term is ((-2)7 =-128). Exam tip: track both sign and power.
Step 3
Exam Tip
हर बार (-2) से गुणा हो रहा है इसलिए आठवाँ पद ((-2)7 =-128) है। संकेत और घात दोनों साथ देखें।
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अनुक्रम \(5,-10,20,-40,\ldots\) में सातवाँ पद क्या है?
What is the seventh term in the sequence \(5,-10,20,-40,\ldots\)?
#sequences
#geometric
#sign-pattern
#class-9
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A (160)
B (-160)
C (320)
D (640)
Explanation opens after your attempt
Step 1
Concept
The general term is (a_n=5(-2)^{n-1}), so (a_7=5(-2)6 =320). Exam tip: an even power gives a positive sign.
Step 2
Why this answer is correct
The correct answer is C. (320). The general term is (a_n=5(-2)^{n-1}), so (a_7=5(-2)6 =320). Exam tip: an even power gives a positive sign.
Step 3
Exam Tip
सामान्य पद (a_n=5(-2)^{n-1}) है इसलिए (a_7=5(-2)6 =320) है। सम घात पर चिह्न धनात्मक होता है।
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अनुक्रम \(1,1,2,3,5,8,\ldots\) में (10)वाँ पद क्या है?
What is the (10)th term in the sequence \(1,1,2,3,5,8,\ldots\)?
#sequences
#fibonacci
#nth-term
#class-9
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A (34)
B (55)
C (89)
D (144)
Explanation opens after your attempt
Step 1
Concept
The next terms are (13,21,34,55), so the (10)th term is (55). Exam tip: write positions when extending Fibonacci-type sequences.
Step 2
Why this answer is correct
The correct answer is B. (55). The next terms are (13,21,34,55), so the (10)th term is (55). Exam tip: write positions when extending Fibonacci-type sequences.
Step 3
Exam Tip
पद आगे (13,21,34,55) हैं इसलिए (10)वाँ पद (55) है। फिबोनाची जैसे अनुक्रम में क्रमांक लिखकर बढ़ें।
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अनुक्रम \(0,2,6,12,20,\ldots\) में (a_n=n(n-1)) है। \(a_{15}\) क्या है?
In the sequence \(0,2,6,12,20,\ldots\), (a_n=n(n-1)). What is \(a_{15}\)?
#sequences
#nth-term
#product-form
#class-9
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A (180)
B (190)
C (200)
D (210)
Explanation opens after your attempt
Step 1
Concept
\(a_{15}=15\times14=210\). Exam tip: substitute the term number for (n) in the formula.
Step 2
Why this answer is correct
The correct answer is D. (210). \(a_{15}=15\times14=210\). Exam tip: substitute the term number for (n) in the formula.
Step 3
Exam Tip
\(a_{15}=15\times14=210\) है। सूत्र में (n) की जगह पद संख्या रखें।
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अनुक्रम \(3,12,27,48,75,\ldots\) का सामान्य पद \(a_n=3n^2\) है। \(a_8-a_6\) क्या है?
The sequence \(3,12,27,48,75,\ldots\) has general term \(a_n=3n^2\). What is \(a_8-a_6\)?
#sequences
#nth-term
#difference
#class-9
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A (72)
B (78)
C (84)
D (90)
Explanation opens after your attempt
Step 1
Concept
\(a_8=192\) and \(a_6=108\), so the difference is (84). Exam tip: find both terms and then subtract.
Step 2
Why this answer is correct
The correct answer is C. (84). \(a_8=192\) and \(a_6=108\), so the difference is (84). Exam tip: find both terms and then subtract.
Step 3
Exam Tip
\(a_8=192\) और \(a_6=108\) इसलिए अंतर (84) है। दोनों पद निकालकर घटाएँ।
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अनुक्रम \(4,10,18,28,40,\ldots\) में अगला पद क्या होगा?
What will be the next term in the sequence \(4,10,18,28,40,\ldots\)?
#sequences
#even-differences
#next-term
#class-9
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A (50)
B (52)
C (54)
D (56)
Explanation opens after your attempt
Step 1
Concept
The differences are (6,8,10,12), so the next difference is (14). Therefore (40+14=54).
Step 2
Why this answer is correct
The correct answer is C. (54). The differences are (6,8,10,12), so the next difference is (14). Therefore (40+14=54).
Step 3
Exam Tip
अंतर (6,8,10,12) हैं इसलिए अगला अंतर (14) होगा। (40+14=54) सही है।
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अनुक्रम \(15,12,7,0,-9,\ldots\) में अंतरों का क्रम \(-3,-5,-7,-9,\ldots\) है। अगला पद क्या होगा?
In the sequence \(15,12,7,0,-9,\ldots\), the differences are \(-3,-5,-7,-9,\ldots\). What will be the next term?
#sequences
#decreasing
#negative-differences
#class-9
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A (20)
B (2)
C (-18)
D (-20)
Explanation opens after your attempt
Step 1
Concept
The next difference is (-11), so (-9-11=-20). Exam tip: always check the negative sign in decreasing sequences.
Step 2
Why this answer is correct
The correct answer is D. (-20). The next difference is (-11), so (-9-11=-20). Exam tip: always check the negative sign in decreasing sequences.
Step 3
Exam Tip
अगला अंतर (-11) होगा इसलिए (-9-11=-20) है। घटते अनुक्रम में ऋण चिह्न की जाँच जरूर करें।
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अनुक्रम \(4,11,22,37,56,\ldots\) में क्रमागत अंतरों का क्रम \(7,11,15,19,\ldots\) है। अगला पद क्या होगा?
In the sequence \(4,11,22,37,56,\ldots\), the successive differences are \(7,11,15,19,\ldots\). What will be the next term?
#sequences
#difference-pattern
#next-term
#class-9
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A (75)
B (77)
C (79)
D (81)
Explanation opens after your attempt
Step 1
Concept
The next difference is (23), so (56+23=79). Exam tip: identifying the difference of differences is the fastest method here.
Step 2
Why this answer is correct
The correct answer is C. (79). The next difference is (23), so (56+23=79). Exam tip: identifying the difference of differences is the fastest method here.
Step 3
Exam Tip
अगला अंतर (23) होगा इसलिए (56+23=79) है। अंतर के अंतर को पहचानना ऐसे प्रश्नों में सबसे तेज तरीका है।
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