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

Question

If a, b, c are three consecutive terms of an AP and x, y, z are three consecutive terms of a GP, then the value of xb -c . yc-a . za-b is (A) 0 (B) xyz (C) -1 (D) 1

Tardigrade Admin · Accepted Answer

Given a , b , c are in A ⋅ P ⇒ b - c =- d , c - a =2 d , a - b =- d And x , y , z are in G.P ⇒ y 2= xz Now xb-c ⋅ yc-a ⋅ za-b =x-d ⋅ y2 d ⋅ z-d =x-d ⋅(x z)d ⋅ z-d=1

Q. If a, b, c are three consecutive terms of an AP and x, y, z are three consecutive terms of a GP, then the value of $x^{b - c} . y^{c - a} . z^{a - b}$ is

0

xyz

-1

1

Given $a, b, c$ are in $A \cdot P$
$\Rightarrow b - c = - d, c - a = 2 d, a - b = - d$
And $x, y, z$ are in $G . P$
$\Rightarrow y^{2} = x z$
Now $x^{b - c} \cdot y^{c - a} \cdot z^{a - b} = x^{- d} \cdot y^{2 d} \cdot z^{- d}$
$= x^{- d} \cdot (x z)^{d} \cdot z^{- d} = 1$

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

0

xyz

-1

1

Given a,b,c are in A⋅P ⇒b−c=−d,c−a=2d,a−b=−d And x,y,z are in G.P ⇒y2=xz Now xb−c⋅yc−a⋅za−b=x−d⋅y2d⋅z−d =x−d⋅(xz)d⋅z−d=1

Q. If a, b, c are three consecutive terms of an AP and x, y, z are three consecutive terms of a GP, then the value of $x^{b - c} . y^{c - a} . z^{a - b}$ is

Given $a, b, c$ are in $A \cdot P$
$\Rightarrow b - c = - d, c - a = 2 d, a - b = - d$
And $x, y, z$ are in $G . P$
$\Rightarrow y^{2} = x z$
Now $x^{b - c} \cdot y^{c - a} \cdot z^{a - b} = x^{- d} \cdot y^{2 d} \cdot z^{- d}$
$= x^{- d} \cdot (x z)^{d} \cdot z^{- d} = 1$