Denote the sequence by

with

.
Recursively:
The first number is

, and each successive number is twice the previous one. So

,

,

, ... .
In other words,



and so in general,

Explicitly:
We can arrive at this formula by, in a way, working backwards. If

, that means

, and so

, and so on. We would end up with

(You'll notice a pattern here: the exponent of the 2 and the index of the earlier term in the sequence add up to

. For example,

.)
or simply

Then the 15th term is obtained immediately by evaluating this rule at

. We get
A geometric progression is also known as a geometric sequence.
Here is a video explaining how you find the n term value.
https://youtu.be/pwUdYEwT9kY
Hope this helps!
Convert the mixed number to inches. 3 feet 8 inches = 44 inches (12 inches per foot x 3 feet= 36 inches + 8 inches= 44 inches). 44 inches (length each section needs to be) x 4 (number of sections needed)=176 inches (total molding needed). To determine the amount of molding needed in feet, convert 176 inches into feet by dividing 176 inches by 12 inches. You get 14 2/3 feet, so the shortest board length is 15 feet.