Question 1197650
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You are on the right track to arrive at d = (b-a)/3
Nice work so far. 


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Given: a,m,n,b form an arithmetic sequence


What this means is:
a = first term
m = second term = a+d
n = third term = m+d = (a+d)+d = a+2d
b = fourth term = n+d = (a+2d)+d = a+3d


Where d is the common difference. It's the length of the gap between terms.
For a more numeric and concrete example, the arithmetic sequence 1,3,5,7,9 has a common difference of d = 2 as this is the gap between terms (eg: 7-5 = 2)
Each time we need a new term to the sequence, add on d.


Let's focus on the line that says
b = fourth term = n+d = (a+2d)+d = a+3d
or in short
b = a+3d


Let's solve for d.
b = a+3d
b-a = 3d
d = (b-a)/3
This matches with what you got. You are correct so far.


Whatever the values of 'a' and b are, we find their difference and split it into 3rds to determine d.
This is to be expected. Imagine a yard stick where we split into 3 equal pieces. The two cut points will be exactly m and n, which represent 1/3 and 2/3 along the entire stick.
'a' and b represent the left most and right most parts of the stick before any cuts were made.
If you're a bit lost, then the visual section below might help clear things up.


We'll use this value of d to determine m and n in terms of 'a' and b only
m = a+d
m = a+(b-a)/3
m = 3a/3 + (b-a)/3
m = (3a+(b-a))/3
<font color=red>m = (2a+b)/3</font>
and
n = a+2d
n = a+2(b-a)/3
n = 3a/3 + (2b-2a)/3
n = (3a+2b-2a)/3
<font color=red>n = (a+2b)/3</font>
It's a bit interesting how we have the swap of coefficients when going from 2a+b to a+2b. 


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Here's a visual to see why this works out
<img src = "https://i.imgur.com/s3XZyEy.png">
In the diagram above, (b-a) represents the length on the number line from 'a' to b
d = (b-a)/3 is the result of splitting this interval into 3 equal pieces.
The cuts are at m and n


In the diagram, I made the distance form 'a' to b exactly 9 units (take note of the grid lines on the graph paper). But you can change this total distance to whatever you like and the same concepts will still apply. 
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