In the sequence $$32, 8, \underline{\phantom{XX}}, \underline{\phantom{XX}}, x,$$each term after the second is the average of the two terms immediately before it. What is the value of $x$?
To find the missing terms, I need to use the definition of average: the sum of the two terms divided by 2. So, for the third term, I add 32 and 8 and divide by 2: $$\frac{32 + 8}{2} = \frac{40}{2} = 20.$$ For the fourth term, I add 8 and 20 and divide by 2: $$\frac{8 + 20}{2} = \frac{28}{2} = 14.$$ For the fifth term, which is $x$, I add 20 and 14 and divide by 2: $$\frac{20 + 14}{2} = \frac{34}{2} = 17.$$ 