If ` G_(1)` is the first of n G.M. s between positive numbers a and b , then show that ` G_(1)^(n+1) = a^(n) b ` .

Explanation

To solve the problem, we need to show that if \( G_1 \) is the first of \( n \) geometric means between two positive numbers \( a \) and \( b \), then:

\[ G_1^{n+1} = a^n b \]

### Step-by-Step Solution:

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