If `a ,b ,c ,d` are in A.P. and `x , y , z` are in G.P., then show that `x^(b-c)doty^(c-a)dotz^(a-b)=1.`

Explanation

To show that \( x^{(b-c)} \cdot y^{(c-a)} \cdot z^{(a-b)} = 1 \) given that \( a, b, c, d \) are in A.P. and \( x, y, z \) are in G.P., we can follow these steps:

### Step 1: Understand the properties of A.P. and G.P.
Since \( a, b, c, d \) are in Arithmetic Progression (A.P.), we have:
\[ 2b = a + c \quad \text{(1)} \]
This means that \( b \) is the average of \( a \) and \( c \).
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