Which recursive rule is correct for the sequence (20,15,10,5,\ldots)?
Answer and explanation
Correct answer: (a_1=20, a_{n+1}=a_n-5)
A recursive rule describes a sequence by giving its starting term and a rule for obtaining each next term from the preceding term. In the sequence \(20,15,10,5,\ldots\), the first term is clearly 20. Comparing consecutive terms shows that each term is 5 less than the term immediately before it.
Starting with \(a_1=20\), the rule \(a_{n+1}=a_n-5\) produces \(a_2=15\), then \(a_3=10\), and then \(a_4=5\), exactly matching the sequence. Adding 5 would make the sequence increase, and starting with 15 would shift every position. Multiplication by 5 also does not fit. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
(a_1=20, a_{n+1}=a_n-5)
Why is this the correct answer?
A recursive rule describes a sequence by giving its starting term and a rule for obtaining each next term from the preceding term. In the sequence \(20,15,10,5,\ldots\), the first term is clearly 20. Comparing consecutive terms shows that each term is 5 less than the term immediately before it.
Starting with \(a_1=20\), the rule \(a_{n+1}=a_n-5\) produces \(a_2=15\), then \(a_3=10\), and then \(a_4=5\), exactly matching the sequence. Adding 5 would make the sequence increase, and starting with 15 would shift every position. Multiplication by 5 also does not fit. Therefore option C is correct.
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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