If (a_1=2) and (a_{n+1}=a_n^2-1), what is (a_3)?
Answer and explanation
Correct answer: 8
In a recursive rule, each new term is calculated from the previous term. First, \(a_2=a_1^2-1=2^2-1=3\). Then \(a_3=a_2^2-1=3^2-1=8\). Therefore, the correct answer is 8. An answer such as 6 may result from subtracting 1 without correctly squaring the previous term. Exam tip: always find \(a_2\) before calculating \(a_3\).
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
In a recursive rule, each new term is calculated from the previous term. First, \(a_2=a_1^2-1=2^2-1=3\). Then \(a_3=a_2^2-1=3^2-1=8\). Therefore, the correct answer is 8. An answer such as 6 may result from subtracting 1 without correctly squaring the previous term. Exam tip: always find \(a_2\) before calculating \(a_3\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
