Which recursive rule matches the sequence (81, 27, 9, 3, ...)?
Answer and explanation
Correct answer: a₁ = 81, aₙ₊₁ = aₙ ÷ 3
A recursive rule must specify the starting term and the operation used to obtain each following term from the preceding term. Here the first term is a₁ = 81. Dividing successively by 3 gives 81 ÷ 3 = 27, 27 ÷ 3 = 9, and 9 ÷ 3 = 3. Therefore the rule is a₁ = 81 and aₙ₊₁ = aₙ ÷ 3, so option C is correct. Option A multiplies by 3, option B starts with 27 rather than 81, and option D subtracts 3, none of which reproduces the complete sequence.
Frequently asked questions
What is the correct answer to this question?
a₁ = 81, aₙ₊₁ = aₙ ÷ 3
Why is this the correct answer?
A recursive rule must specify the starting term and the operation used to obtain each following term from the preceding term. Here the first term is a₁ = 81. Dividing successively by 3 gives 81 ÷ 3 = 27, 27 ÷ 3 = 9, and 9 ÷ 3 = 3. Therefore the rule is a₁ = 81 and aₙ₊₁ = aₙ ÷ 3, so option C is correct. Option A multiplies by 3, option B starts with 27 rather than 81, and option D subtracts 3, none of which reproduces the complete sequence.
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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