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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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