Given that the sequence is given by m+3,3m and 6m-8 to get the value of m that will make the sequence an arithmetic sequence we proceed as follows;
arithmetic sequences have the same common differences;
that is:
3m-(m+3)=(6m-8)-3m
thus solving for the value of me we get:
3m-m-3=6m-8-3m
2m-3=6m-3m-8
2m-3=3m-8
collecting like terms we get:
2m-3m=-8+3
-m=-5
thus
m=5
the answer is m=5
