Geometric Series and Applications

 Find the common ratio

What is the sum of the first three terms of the sequence 3, 15, 75,375...?

Find the sum of the geometric series.

2 + 12 + 72 + 432

What is the value of S₁₀ for the following geometric series:

2-6+18-54+...

What is x, the second term in the geometric series  $$\frac{1}{4}$$ +  x  +  $$\frac{1}{36}$$ +  $$\frac{1}{108}$$ + ... ?
(Note: In a geometric series the ratio of any term to the following term is constant.)

Find the sum of the infinite geometric series, if it exists.

$$\sum_{k=1}^{\infty}\left(\frac{4}{5}\right)^{k-1}$$  Find the sum of the series if it exists.

Evaluate the geometric series described below.
 

Evaluate the geometric series below:
4 - 8 - 16 - 32...,  S₇