Q. 20

If ax = by = cz, x ≠ 0, y ≠ 0, z ≠ 0 and b2 = ac, then show that are in A.P.

Answer :

Let ax = by = cz = k.


We know that if am = k, then a = .


a = , b = , c =


Given, b2 = ac


= ×


We know that (am)n = amn and am × an = am + n.


=


Bases are same, so we equate the powers.


= +


+ = +


- = -


We know that when t1, t2, t3 … are in A.P., t3 – t2 = t2 – t1


, and are in A.P.


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