9.3 Geometric Sequences

Geometric Sequence: a sequence of numbers made by multiplying by some value each time.
- "Some value" is the common ratio (r)

ex. 3, 6, 12, 24, 48, 96, .....

The difference between each term is found by dividing by 2 each time, making the common ratio 2. 3 x 2 = 6
6 x 2 = 12, ect.

Explicit Formula
*always exponential*












so,



Ex.
3, 6, 12, 24, 48, 96, ...

r=2

so the explicit formula would be:




Finding the nth Term




To find the nth term, take the first value of the geometric sequence and multiply it by the quantity of one minus the common ratio to the nth term, divided by one minus the common ratio.

Ex.

3, 6, 12, 24, 48, ...

r=2

Finding the 6th term:






Summation Notation

Finding the nth partial sum of a geometric sequence:






Where



is the explicit formula.