The sequence 4, 10, 16,... is an arithmetic sequence because there is a common difference between every pair of consecutive terms. To find the common difference, we can subtract any term from the following term. For example:
- The common difference between the first and second terms is 10 - 4 = 6.
- The common difference between the second and third terms is 16 - 10 = 6.
Since the common difference is 6, we can find the nth term of the sequence using the formula:
nth term = first term + (n - 1) * common difference
The first term is 4 and the common difference is 6, so we get:
nth term = 4 + (n - 1) * 6
Simplifying this expression, we get:
nth term = 6n - 2
Therefore, the correct answer is (A) 2(3n-1).