If `a ,b ,c ,d` are in G.P. prove that: `(a^2+b^2),(b^2+c^2),(c^2+d^2)` are in G.P. `(a^2-b^2),(b^2-c^2),(c^2-d^2)` are in G.P. `1/(a^2+b^2),1/(b^2+c^2),1/(c^2+d^2)` are in G.P.

Explanation

To prove that if \( a, b, c, d \) are in G.P., then the following sets of expressions are also in G.P.:

1. \( (a^2 + b^2), (b^2 + c^2), (c^2 + d^2) \)
2. \( (a^2 - b^2), (b^2 - c^2), (c^2 - d^2) \)
3. \( \left( \frac{1}{a^2 + b^2}, \frac{1}{b^2 + c^2}, \frac{1}{c^2 + d^2} \right) \)

### Step 1: Express \( b \) and \( c \) in terms of \( a \) and \( r \)

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