What will be the 10th term in the sequence (1, 4, 2, 8, 3, 16, 4, ...)?
Answer and explanation
Correct answer: 64
The governing concept is recognizing an alternating or interleaved sequence. Separate the odd and even positions. At odd positions we have 1, 2, 3, 4, ...; therefore the term at position 2k - 1 is k. At even positions we have 4, 8, 16, 32, ...; this is a geometric progression with first term 4 and ratio 2, so the term at position 2k is 4 multiplied by 2^(k - 1). Since 10 = 2(5), the 10th term is the fifth even-position term: 4, 8, 16, 32, 64. Thus option B is correct. Options A, C, and D correspond to taking the fourth or sixth even-position term or doubling one time too many.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The governing concept is recognizing an alternating or interleaved sequence. Separate the odd and even positions. At odd positions we have 1, 2, 3, 4, ...; therefore the term at position 2k - 1 is k. At even positions we have 4, 8, 16, 32, ...; this is a geometric progression with first term 4 and ratio 2, so the term at position 2k is 4 multiplied by 2^(k - 1). Since 10 = 2(5), the 10th term is the fifth even-position term: 4, 8, 16, 32, 64. Thus option B is correct. Options A, C, and D correspond to taking the fourth or sixth even-position term or doubling one time too many.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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