The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
\[
a_{n}=n-16
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The sequence is arithmetic with a common difference of
B. The sequence is geometric with a common ratio of
c. The sequence is neither arithmetic nor geometric.
Answer
Final Answer: The sequence is arithmetic with a common difference of \(\boxed{1}\).
Step 1 ：The given sequence is \(a_{n}=n-16\). This is a linear function of \(n\), which suggests that the sequence is arithmetic.
Step 2 ：In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term.
Step 3 ：The difference between consecutive terms can be found by subtracting \(a_{n}\) from \(a_{n+1}\), which gives \(a_{n+1} - a_{n} = (n+1-16) - (n-16) = 1\).
Step 4 ：Therefore, the common difference is 1.
Step 5 ：Final Answer: The sequence is arithmetic with a common difference of \(\boxed{1}\).
