Sure, let's solve the problem step-by-step.
1. Understanding Arithmetic Sequence:
An arithmetic sequence is a sequence of numbers in which the difference of any two successive numbers is constant. This difference is called the "common difference."
2. Identify the given terms:
Here, we have three terms in the arithmetic sequence:
- The first term [tex]\( a = 25 \)[/tex]
- The second term [tex]\( b = m \)[/tex]
- The third term [tex]\( c = 35 \)[/tex]
3. Set up the relationship for arithmetic sequence:
For an arithmetic sequence, the difference between successive terms is the same. This means:
[tex]\[
b - a = c - b
\][/tex]
In this case:
[tex]\[
m - 25 = 35 - m
\][/tex]
4. Solve the equation:
[tex]\[
m - 25 = 35 - m
\][/tex]
Add [tex]\( m \)[/tex] to both sides of the equation:
[tex]\[
2m - 25 = 35
\][/tex]
Then add 25 to both sides to isolate the term with [tex]\( m \)[/tex]:
[tex]\[
2m = 60
\][/tex]
Now, divide both sides by 2:
[tex]\[
m = 30
\][/tex]
So, the value of [tex]\( m \)[/tex] is [tex]\( 30 \)[/tex].
