<PRE><B>Question 1084924</B>
in an arithmetic sequence, the difference between the term and the next term is the same for all terms in the sequence.


your sequence is:


6-2m
2m+1
5m


if the common difference is d, then you get.


2m+1 = 6 - 2m + d


5m = 2m + 1 + d


solve for d in both equations to get:


d = 2m + 1 - 6 + 2m


d = 5m - 2m - 1 


combine like terms to get:


d = 4m - 5
d = 3m - 1


subtract the second equation from the first to get:


0 = m - 4


solve for m to get:


m = 4


when m = 4:

6 - 2m = -2
2m + 1 = 9
5m = 20


9 - -2 = 11
20 - 9 = 11


the common difference is 11.


the value of m equal to 4 is confirmed as good.


as a bonus, we also got the value of d, which is 11.


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