Q. 20

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

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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