# Math Help - Arithmetic Mean

1. ## Arithmetic Mean

If a < b, show that a < (a + b)/2 < b. The number (a + b)/2 is called the ARITHMETIC MEAN of a and b.

2. Originally Posted by symmetry
If a < b, show that a < (a + b)/2 < b. The number (a + b)/2 is called the ARITHMETIC MEAN of a and b.
Since $a

Then: $2a

So: $a<\frac{a+b}{2}$

Also since $a

Then: $a+b<2b$

So: $\frac{a+b}{2}

Therefore: $a<\frac{a+b}{2}

3. ## ok

Very interesting notes in this prove question and answer.