How do you determine whether the sequence #9/4, 2, 7/4, 3/2, 5/4,...# is arithmetic and if it is, what is the common difference?

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Answer 1 · 2017-02-17T10:48:44

It is an arithmetic sequence
The common difference is #-1/4#

So that we can make a direct comparison make all the denominators the same giving:

#9/4"; "8/4"; "7/4"; "6/4"; "5/4#

Observe that in each case the next term is #1/4# less.

As this difference is consistent then it is an arithmetic sequence.
The common difference is #-1/4#. The minus sign is very important.

#8/4-9/4=-1/4#

#7/4-8/4=-1/4#

#6/4-7/4=-1/4#

#5/4-6/4=-1/4#