What is the recursive rule for the sequence 2, 4, 8, 16, ...?
Answer and explanation
Correct answer: a_1 = 2, a_(n+1) = 2a_n
A recursive rule describes the first term and the operation that produces each following term. The first term is 2. Comparing consecutive terms shows 4=2×2, 8=2×4, and 16=2×8, so each term is twice the preceding term. Consequently, the correct rule is a_1=2 and a_(n+1)=2a_n, which is option B. Option A describes adding 2 and would produce 2, 4, 6, 8 rather than the given sequence. Option C has the wrong starting term, and option D produces decreasing values.
Frequently asked questions
What is the correct answer to this question?
a_1 = 2, a_(n+1) = 2a_n
Why is this the correct answer?
A recursive rule describes the first term and the operation that produces each following term. The first term is 2. Comparing consecutive terms shows 4=2×2, 8=2×4, and 16=2×8, so each term is twice the preceding term. Consequently, the correct rule is a_1=2 and a_(n+1)=2a_n, which is option B. Option A describes adding 2 and would produce 2, 4, 6, 8 rather than the given sequence. Option C has the wrong starting term, and option D produces decreasing values.
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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