According to the recursive rule in the sequence (32, 16, 8, 4, ...), what is the next term?
Answer and explanation
Correct answer: 2
The governing pattern is recursive division by a constant. Compare consecutive terms: 16 = 32 ÷ 2, 8 = 16 ÷ 2, and 4 = 8 ÷ 2. Therefore the next term is obtained from the last known term by the same operation: 4 ÷ 2 = 2. Hence option B is correct. Option A would require another division by 2 after reaching 2, option C does not follow the constant ratio, and option D merely repeats the current term. The sequence is also a geometric sequence with common ratio one-half, although the question specifically focuses on its recursive rule.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The governing pattern is recursive division by a constant. Compare consecutive terms: 16 = 32 ÷ 2, 8 = 16 ÷ 2, and 4 = 8 ÷ 2. Therefore the next term is obtained from the last known term by the same operation: 4 ÷ 2 = 2. Hence option B is correct. Option A would require another division by 2 after reaching 2, option C does not follow the constant ratio, and option D merely repeats the current term. The sequence is also a geometric sequence with common ratio one-half, although the question specifically focuses on its recursive rule.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
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