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

User Equan
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1 Answer

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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
User Roney Michael
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