Q. 1 A

If are in A.P., prove that:

are in A.P.

Answer :

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


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