Determine whether the sequence is arithmetic or geometric. Sequence 1: –10, 20, – 40, 80, ... Sequence 2: 15, – 5, – 25, – 45, ... Which of the following statements are true regarding Sequence 1 and Sequence 2. A) Sequence 2 is arithmetic and Sequence 1 is geometric. B) Both sequences are arithmetic. C) Both sequences are geometric. D) Sequence 1 is arithmetic and Sequence 2 is geometric.

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Determine whether the sequence is arithmetic or geometric. Sequence 1: –10, 20, – 40, 80, ... Sequence 2: 15, – 5, – 25, – 45, ... Which of the following statements are true regarding Sequence 1 and Sequence 2. A) Sequence 2 is arithmetic and Sequence 1 is geometric. B) Both sequences are arithmetic. C) Both sequences are geometric. D) Sequence 1 is arithmetic and Sequence 2 is geometric.

Mathematics
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Haha, well there is a nice way to check this, lets look at the first sequence \[-10, 20, -40, 80, ...\] do you see a pattern here?

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yes I do.
Ok well lets look at the first two terms, -10, 20 notice if you multiply -10 by -2 you will get 20? Would the same work if you multiply 20 by -2 to get the next term (-40)?
Basically it's an arithmetic sequence if \[t_2-t_1 = t_3 - t_1\]and it's a geometric sequence if \[\frac{ t_2 }{ t_1 } = \frac{ t_3 }{ t_2 }\] that gives you your common ratio. Where the t represents the term, and the subscript is the address of the term, so \[t_1 = -10~~~t_2 = 20\] etc
an arithmetic sequence has the same difference between the terms and the geometric sequence has the same ratio between the terms.
in an arithmetic sequence, the next number is found by multiplying...and each term has to be multiplied by the same number. In a geometric sequence, the next number is found by dividing...and each term has to be divided by the same number.

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