In the sequence (4, 6, 9, 14, 21, 32, …), the successive differences are prime numbers (2, 3, 5, 7, 11, …). What will be the next term?
Answer and explanation
Correct answer: 45
The governing concept is using successive differences to extend a sequence. Subtracting consecutive terms gives 6 − 4 = 2, 9 − 6 = 3, 14 − 9 = 5, 21 − 14 = 7, and 32 − 21 = 11. These are consecutive prime numbers. The next prime after 11 is 13, so the next term must be the current final term plus 13: 32 + 13 = 45. Therefore option C is correct. The distractor 41 would add 9, 43 would add 11 by repeating the previous difference, and 47 would add 15; none follows the stated prime-difference pattern. Writing the differences separately avoids confusing terms with increments.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
The governing concept is using successive differences to extend a sequence. Subtracting consecutive terms gives 6 − 4 = 2, 9 − 6 = 3, 14 − 9 = 5, 21 − 14 = 7, and 32 − 21 = 11. These are consecutive prime numbers. The next prime after 11 is 13, so the next term must be the current final term plus 13: 32 + 13 = 45. Therefore option C is correct. The distractor 41 would add 9, 43 would add 11 by repeating the previous difference, and 47 would add 15; none follows the stated prime-difference pattern. Writing the differences separately avoids confusing terms with increments.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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