Is this a arithmetic sequence or a geometric sequence??

Question

So I got this math question from my Math teacher and in the question it labels it as a geometric sequence, by in the description of it it says it goes down by a flat 5% every time.  So from the definitions I know and I went over them multiple times, it should be an arithmetic sequence, not a geometric sequence.  Here's the question itself:

The colour of some clothing fades over time when washed.  Suppose a pair of jeans fades by 5% with each washing.

 

If I am correct the way that is described that is an arithmetic sequence, if I am missing anything please let me know because I am very much stuck on this in my math and need to catch up so any help would be appreciated.

Answer 1

PLZ check the important difference between Arithmetic Sequence and Geometric Sequence (from Wikipedia):

 

  Arithmetic Sequence -- "a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.

 

  A Geometric Sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.

 

 

The statement, "goes down by a flat 5% every time" means that each term is 95% of the previous term.  That difference is not a constant value (obtained by simple subtraction), but a percent of the previous term (obtained by multiplication).

 

Note that an Arithmetic Sequence forms a line when (term number, term value) is plotted.

 

A percent describes a common ratio. Thus, "goes down by 5%" means that:

     ( (this term) - (last term) ) / (last term)  =  -5%           

          [note: this is "-" because this term is smaller than last term]

 

The problem does not give values for "this term" or "last term," but if there were some number to express the colour of the jeans, an Arithmetic Sequence would insist that the difference between term values would be constant.