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SubjectsMathematics
अनुक्रम
In this Class 9 Mathematics topic from Sequences and Progressions, students learn how numbers or objects are arranged in a definite order and how to identify the rule connecting successive terms. They practise finding missing terms, writing a sequence from a given pattern, and expressing its general term when the relationship is clear. The topic develops pattern recognition, logical reasoning, and accuracy, while preparing students to understand progressions and solve sequence-based problems in later mathematics.
Correct answer: A. 10
Explanation: The difference between each pair of consecutive terms is 2: 4−2=2, 6−4=2, and 8−6=2. Therefore, adding 2 to 8 gives the next term, 10. Although 12 is also even, it would be obtained by adding 4 to 8. Exam tip: First check the difference between consecutive terms in a sequence.
Correct answer: B. 25
Explanation: The terms are 5, 10, 15, 20, 25. Each new term is 5 more than the previous term, so the fifth term is 25. Note that 20 is the fourth term, not the fifth. Exam tip: Count terms starting from the first given term.
Correct answer: C. 7
Explanation: The terms of the sequence are 1, 3, 5, 7, ... . Thus, the first term is 1, the second is 3, the third is 5, and the fourth term is 7. The number 9 is the next, or fifth, term. Exam tip: To find a term number, count the terms in order from the left.
Correct answer: C. 50
Explanation: In this sequence, each term is 10 greater than the previous term: 10, 20, 30, 40. Therefore, adding 10 to 40 gives the next term, 50. Option 45 is not correct because it would make the difference only 5. Exam tip: To find the next term, check the difference between consecutive terms.
Correct answer: A. 8
Explanation: Each term in the sequence is 1 less than the previous term: 12, 11, 10, 9. Therefore, the term after 9 is 8. Although 7 also occurs in the sequence, it is the term after 8, not the next term. Exam tip: Compare consecutive terms to identify the rule of a sequence.
Correct answer: B. 24
Explanation: Each successive term in the sequence is 4 greater than the previous term. The terms are 4, 8, 12, 16, 20, 24. Therefore, the sixth term is 24. The number 20 is the fifth term, so it is a close but incorrect option. Exam tip: Write and count the terms in order to avoid confusing adjacent terms.
Correct answer: C. 21
Explanation: The terms of the sequence are 7, 14, 21, 28, \ldots. Thus, 7 is the first term, 14 the second term, and 21 the third term. 28 is the fourth term, so it is a close but incorrect option. Exam tip: Count the positions of the terms from left to right.
Correct answer: D. 18
Explanation: Each term is 3 less than the preceding term: 30, 27, 24, 21. Therefore, 21 - 3 = 18, so 18 is the correct answer. Getting 19 or 20 would require subtracting 2 or 1, which does not match the given pattern. Exam tip: find the difference between consecutive terms to identify the rule of a sequence.
Correct answer: A. 9
Explanation: The terms 9, 18, 27, and 36 can be written as \(9\times1\), \(9\times2\), \(9\times3\), and \(9\times4\), respectively. Therefore, every term is a multiple of 9. Although 3 is also a factor of all these terms, the sequence follows the pattern of consecutive multiples of 9; 6 is not a factor of 27. Exam tip: Write the terms as a common number multiplied by \(1,2,3,\ldots\) to identify the sequence pattern.
Correct answer: B. 60
Explanation: In this sequence, each term is 10 less than the previous term: 100, 90, 80, 70. Therefore, 70 - 10 = 60, so the correct answer is 60. The value 50 would be obtained after subtracting 10 twice, so it is not the next term. Exam tip: Compare consecutive terms to identify the rule of a sequence.
Correct answer: C. 11
Explanation: The terms of the sequence are 2, 5, 8, and 11 in order. Therefore, the fourth term is 11. The number 14 would be the next, or fifth, term. In exams, count the terms as 1st, 2nd, 3rd, and 4th to identify the required position.
Correct answer: C. 27
Explanation: The terms are 15, 18, 21, and 24, and each next term is 3 more than the previous term. Therefore, the fifth term is 24 + 3 = 27. Option 28 is incorrect because it would make the difference after 24 equal to 4. Exam tip: Check the common difference between the given terms before finding the next term.
Correct answer: A. 30
Explanation: Check the difference between consecutive terms: 45 - 50 = -5, 40 - 45 = -5, and 35 - 40 = -5. Thus, each next term is 5 less than the previous term. Therefore, 35 - 5 = 30, so the correct answer is 30. The number 25 would come after 30 on subtracting 5 again. Exam tip: To find the next term in a sequence, first check the difference between consecutive terms.
Correct answer: B. 12
Explanation: The terms of the sequence are counted from left to right: 6 is the first term, 12 is the second, 18 is the third, and 24 is the fourth. Therefore, 12 is the correct answer. Although 18 is a nearby term, it is the third term, not the second. Exam tip: Always count terms in a sequence from the left.
Correct answer: C. 13
Explanation: Each term is obtained by adding 3 to the preceding term: 1, 4, 7, 10. Therefore, the next term is 10 + 3 = 13. Choosing 12 would give a difference of 2, which does not follow the pattern. Exam tip: Compare consecutive terms to identify the rule of a sequence.
Correct answer: B. 20
Explanation: Each successive term is 5 less than the previous one: 40, 35, 30, 25, 20. Therefore, the fifth term is 20. The number 25 is the fourth term, so it is not correct. Exam tip: Write and count the terms in order to avoid errors in term position.
Correct answer: B. 18
Explanation: This is an arithmetic sequence in which each term is 3 more than the previous term. The terms are 3, 6, 9, 12, 15, 18. Therefore, the sixth term is 18. Although 15 is close, it is the fifth term. Exam tip: While counting terms, count the first term as term 1.
Correct answer: C. 14
Explanation: Each term in the sequence is 2 less than the preceding term: 22, 20, 18, 16. Therefore, 16 - 2 = 14, so the correct answer is 14. Choosing 15 would mean subtracting only 1 from 16, which does not follow the pattern. Exam tip: Compare consecutive terms to identify the rule of a sequence.
Correct answer: C. 40
Explanation: In this sequence, each term is 8 greater than the previous one: 8, 16, 24, 32, 40. Therefore, the fifth term is 40. Although 42 is close, it would result from adding 10 to 32; the common difference here is 8. Exam tip: Find the difference between consecutive terms to identify the next term quickly.
Correct answer: A. 10
Explanation: In this sequence, each term is 1 less than the preceding term: 14, 13, 12, 11. Therefore, subtracting 1 from 11 gives the next term, 10. Choosing 9 would mean a decrease of 2 from 11, which does not follow the given pattern. Exam tip: Compare consecutive terms to identify the rule of a sequence.
Correct answer: C. 44
Explanation: The terms of the sequence are 11, 22, 33, and 44 in order. Therefore, the fourth term is 44. The number 55 would be the next, or fifth, term. In exams, count term positions starting from the first term.
Correct answer: B. 18
Explanation: In this sequence, each term is 3 greater than the preceding term: 6, 9, 12, 15. Therefore, 15 + 3 = 18, so 18 is correct. Choosing 17 would give a difference of 2, which does not match the constant difference in the sequence. Exam tip: Find the difference between consecutive terms to identify the next term.
Correct answer: C. 12
Explanation: Each term in the sequence is 4 less than the preceding term: 28, 24, 20, 16. Therefore, 16 - 4 = 12, so 12 is correct. Choosing 14 would give a difference of only 2, which does not match the pattern. Exam tip: Find the difference between consecutive terms to identify the pattern.
Correct answer: C. 33
Explanation: The common difference between consecutive terms is 5: 18 − 13 = 5 and 23 − 18 = 5. Therefore, adding 5 to the fourth term, 28, gives the fifth term as 33. Option 32 would result from adding only 4, so it is incorrect. Exam tip: Check the difference between consecutive terms before finding the next term.
Correct answer: C. 50
Explanation: Each term is 10 less than the preceding term: 90, 80, 70, 60. Therefore, 60 - 10 = 50, so the correct answer is 50. Choosing 45 would give a difference of 15, which does not match the common difference in the sequence. Exam tip: Find the difference between consecutive terms to identify the next term quickly.
