Identifying the Series Pattern
- The given series is 16, 8, 4, ... , 1/2^17
- To find the pattern, we can see that each term is half of the previous term

Finding the Common Ratio
- The common ratio between each term can be calculated by dividing a term by its previous term
- For example, 8/16 = 1/2, 4/8 = 1/2, and so on

Expressing the nth Term
- The nth term of a geometric series can be expressed as: a * r^(n-1), where a is the first term and r is the common ratio
- In this case, a = 16 and r = 1/2
- So, the nth term can be written as: 16 * (1/2)^(n-1)

Finding the Value of n
- Given that the nth term is 1/2^17, we can set up the equation: 16 * (1/2)^(n-1) = 1/2^17
- Simplifying the equation, we get: 16 * 1/2^(n-1) = 1/2^17
- Dividing both sides by 16, we have: 1/2^(n-1) = 1/2^17
- Comparing the powers of 2, we get: n - 1 = 17
- Therefore, n = 18
Thus, the value of n in the series 16, 8, 4, ... , 1/2^17 is 18.