If (a_1=3), (a_2=5), and (a_n=a_{n-1}+a_{n-2}), what is (a_6)?
Answer and explanation
Correct answer: (34)
A recursive rule defines a term by using earlier terms. Here, every term after the first two is found by adding the two immediately preceding terms. The starting values are already given, so the sequence can be built one position at a time. Keeping the position labels visible helps prevent skipping a term or confusing the required term with the previous one.
Start with \(a_1=3\) and \(a_2=5\). Then \(a_3=3+5=8\), \(a_4=5+8=13\), \(a_5=8+13=21\), and \(a_6=13+21=34\). Therefore the correct choice is D, \(34\). The other numerical choices result from stopping too early or making an addition error.
Frequently asked questions
What is the correct answer to this question?
(34)
Why is this the correct answer?
A recursive rule defines a term by using earlier terms. Here, every term after the first two is found by adding the two immediately preceding terms. The starting values are already given, so the sequence can be built one position at a time. Keeping the position labels visible helps prevent skipping a term or confusing the required term with the previous one.
Start with \(a_1=3\) and \(a_2=5\). Then \(a_3=3+5=8\), \(a_4=5+8=13\), \(a_5=8+13=21\), and \(a_6=13+21=34\). Therefore the correct choice is D, \(34\). The other numerical choices result from stopping too early or making an addition error.
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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