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If a, b, c are three consecutive terms of an AP and x, y, z are three consecutive terms of GP, then the value of xb - c yc - a  za - b is

If a, b, c are three consecutive terms of an AP and x, y, z are three consecutive terms of GP, then the value of xb - c yc - a  za - b is Correct Answer 1

Concept:

If a, b, c and three consecutive terms of an AP then b - a = c - b = d (Common difference)

If x, y, z are three consecutive terms of GP then y2 = xz

 

Calculations:

Given, a, b, c and three consecutive terms of an AP.

⇒ b - a = c - b = d(Common difference)

So, a = a

b = a + d

c = a + 2d

Now, c - a = 2d, a - b = -d, b - c = -d

x, y, z are three consecutive terms of GP

⇒ y2 = xz

Now, consider xb - c yc - a za - b 

= x-d yc - a z -d

= (xz) -d y2d

= (y2) -d y2d                      ( ∵y 2 = xz)         

= y-2d y2d

= y0

= 1

Hence, If a, b, c and three consecutive terms of an AP and x, y, z are three consecutive terms of GP, then the value of xb - c yc - a za - b = 1

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