SOLUTION: How can I find the value of m if 6-2m, 2m+1 and 5m form an arithmetic sequence?

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Question 1084924: How can I find the value of m if 6-2m, 2m+1 and 5m form an arithmetic sequence?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

How can I find the value of m if 6-2m, 2m+1 and 5m form an arithmetic sequence?

As this is an AP, we get:
2m + 1 - (6 - 2m) = 5m - (2m + 1)
2m + 1 - 6 + 2m = 5m - 2m - 1
4m - 5 = 3m - 1
4m - 3m = - 1 + 5 ======>