Question

If a b and c are in AP then find the arithmetic mean of a and c

Answer 1

if there are three numbers a, b, c then b=a+c/2

Answer 2

The arithmetic mean of a and c = b

Step-by-step explanation:

Given,

a b and c are in AP.

To find, the arithmetic mean of a and c = ?

a b and c are in AP.

∴ b - a = c - b

⇒ 2b = a + c          ........ (1)

The arithmetic mean of a and c

= $\dfrac{a+c}{2}$

Using equation (1), we get

= $\dfrac{2b}{2}$

= b

∴ The arithmetic mean of a and c = b

Thus, the arithmetic mean of a and c is b.