If a₁ = 90 and aₙ₊₁ = aₙ ÷ 3, what is a₃?
Answer and explanation
Correct answer: 10
To evaluate a recursively defined sequence, apply the stated operation once for each transition between the starting index and the requested index. The sequence begins with a₁ = 90. Applying the rule once gives a₂ = 90 ÷ 3 = 30. Applying it a second time gives a₃ = 30 ÷ 3 = 10. Therefore option A is correct. Option C is the value of a₂, so it results from stopping one step too early. Option B does not arise from division by 3. Option D would be obtained by dividing a₃ by 3 once more, so it corresponds to a₄ rather than a₃. Correct indexing is essential in recurrence questions.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
To evaluate a recursively defined sequence, apply the stated operation once for each transition between the starting index and the requested index. The sequence begins with a₁ = 90. Applying the rule once gives a₂ = 90 ÷ 3 = 30. Applying it a second time gives a₃ = 30 ÷ 3 = 10. Therefore option A is correct. Option C is the value of a₂, so it results from stopping one step too early. Option B does not arise from division by 3. Option D would be obtained by dividing a₃ by 3 once more, so it corresponds to a₄ rather than a₃. Correct indexing is essential in recurrence questions.
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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