Problem

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.

Solution

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 \(\boxed{1}\).

From Solvely APP
Source: https://solvelyapp.com/problems/16751/

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