Finding the Value of n in a Series
The given series is 16, 8, 4, ...

Identifying the Pattern
The series appears to be decreasing by half each time. This is because each term is half of the previous term.

Finding the nth Term
To find the nth term of the series, we can use the formula for the nth term of a geometric sequence:
\[ a_n = a_1 \times r^{(n-1)} \]
Where:
- \( a_n \) is the nth term
- \( a_1 \) is the first term
- \( r \) is the common ratio
- \( n \) is the term number

Substituting Given Values
In this case, the first term (\( a_1 \)) is 16, the common ratio is 0.5 (since each term is half of the previous one), and we need to find the term number (\( n \)) when the nth term is 1/2^17.
Substitute the values into the formula:
\[ 1/2^{17} = 16 \times (0.5)^{(n-1)} \]
Simplify:
\[ 1/2^{17} = 8 \times (0.5)^n \]

Solving for n
We need to find the value of n in the equation above. To do this, we can express both sides with the same base:
\[ 1/2^{17} = 2^{-17} \]
Now we can compare the powers of 2 on both sides of the equation:
\[ 2^{-17} = 8 \times 2^{-n} \]
Since 8 can be expressed as \( 2^3 \), we have:
\[ 2^{-17} = 2^3 \times 2^{-n} \]
\[ 2^{-17} = 2^{3-n} \]
Equating the powers of 2:
\[ -17 = 3 - n \]
\[ n = 3 + 17 \]
\[ n = 20 \]

Conclusion
Therefore, the value of n in the given series is 20.