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Algebra Difficulty 2.9 Junior Find the answer

The general term formula for the sequence +3, -7, 11, -15... could be

Pick one

Solutions — 3

Solution 1

The absolute values of the terms in the sequence +3, -7, 11, -15... are
3, 7, 11, 15...
Therefore, an=4n1a_n=4n-1,
The general term formula for the sequence +3, -7, 11, -15... can be an=(1)n+1(4n1)a_n=(-1)^{n+1}(4n-1)
Hence, the correct option is D\boxed{D}.

Solution 2

For the sequence +3, -7, 11, -15..., the absolute values of the terms are
3, 7, 11, 15...
Therefore, an=4n1a_n = 4n - 1,
The general term formula for the sequence +3, -7, 11, -15... can be an=(1)n+1(4n1)a_n = (-1)^{n+1}(4n - 1)
Hence, the correct option is D\boxed{D}
Analysis: First, determine (1)n+1(-1)^{n+1} based on the signs of the terms, and then, since the absolute values form an arithmetic sequence, the general term formula of the sequence can be determined.

Solution 3

Solution: For the sequence +3, -7, 11, -15..., the absolute values of the terms are
3, 7, 11, 15...
Therefore, an=4n1a_n = 4n-1,
The general term formula for the sequence +3, -7, 11, -15... can be an=(1)n+1(4n1)a_n = (-1)^{n+1}(4n-1)
Hence, the correct choice is D\boxed{D}
First, determine (1)n+1(-1)^{n+1} based on the signs of the terms, and then, since the absolute values form an arithmetic sequence, the general term formula for the sequence can be determined.
This question mainly tests the ability to find the general term formula of a sequence. The key is to determine (1)n+1(-1)^{n+1} based on the signs of the terms, and that the absolute values form an arithmetic sequence, then multiply to find the general term formula of the sequence.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.