We know, if a, b, c are in AP,

Then b - a = c - b

It is said that, are in AP,

Hence,

If are in AP, then

Taking LCM,

Now, LHS =

Multiply c in both numerator and denominator,

We get,

RHS

Multiply a in both numerator and denominator,

We get, =

Therefore, LHS = RHS

=

c(b - a) = a(b-c)

Also,

c(b - a) = a(b - c)

Hence given terms are in AP