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8 July, 23:56

The following is a geometric sequence 5,3,1,-1

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  1. 9 July, 00:00
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    No it is not. All geometric sequences have a common ratio that is a constant found when you divide any term by the previous one.

    3/5!=1/3

    So it is not a geometric sequence.

    It IS an arithmetic sequence though, as all arithmetic sequences have a common difference that is a constant found when you find the difference between any term and the term preceding it.

    3-5=1-3=-1-1=d=2

    So there is a common difference of 2 so this is an arithmetic sequence. And all arithmetic sequences can be expressed as:

    a (n) = a+d (n-1), a (n) = nth term, a=initial term, d=common difference, n=term number, in this case a=5 and d=-2 so

    a (n) = 5-2 (n-1) which of course can be simplified ...

    a (n) = 5-2n+2

    a (n) = 7-2n
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