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Geometric Progressions

A geometric progression is a sequence of numbers where the previous term is multiplied by a constant to get the next term. 1, 2, 4, 8,... is a geometric sequence where each term is multiplied by 2.

Geometric Mean

         

What is the geometric mean of 5 and 45?

What is the geometric mean of the following numbers:

\[ 63, 147, 27 \]

There is a cuboid with dimensions \( 10 \times a \times b. \) If \[10, a, b\] form a geometric progression and the volume of the cuboid is \( 1000, \) what is the value of \(a?\)

What is the geometric mean of \({4}^1, {4}^2, \cdots, {4}^n?\)

What is the geometric mean of the following numbers:

\[ 16, 12, 9 ? \]

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