Question

Find the single arthmetic mean between (a-b) and (a+b)

Answer 1

Hey there!

To find n-arithmetic mean between a & b , The common difference is d. d is given by, $d = \frac{b - a}{n + 1}$

Here, Number of arithmetic means = 1 , So d = b - a / 2

Now,

$d = \frac{a + b - (a - b)}{2} \\ \\ d = \frac{2b}{2} = b$

So , Single arithmetic mean between ( a + b) and ( a -b) = ( a - b) + b = a.

Short method

Single arithmetic mean between x, y is (x + y)/2.

So, Single arithmetic mean =
$\frac{(a + b) + (a - b)}{2} \\ \\ = \frac{2a}{2} = a$

Single arthmetic mean between (a-b) and (a+b) is a