If a, b, c and d are in G.P. show that `(a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2`.

Explanation

To prove that \((a^2 + b^2 + c^2)(b^2 + c^2 + d^2) = (ab + bc + cd)^2\) given that \(a, b, c, d\) are in geometric progression (G.P.), we can follow these steps:

### Step 1: Express \(b\), \(c\), and \(d\) in terms of \(a\) and the common ratio \(r\)
Since \(a, b, c, d\) are in G.P., we can express them as:
- \(b = ar\)
- \(c = ar^2\)
- \(d = ar^3\)

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