Final answer:
The nth term of the sequence 2, 6, 10, 14... is given by the formula a(n) = 2 + 4(n-1), representing an arithmetic sequence with a common difference of 4.
Step-by-step explanation:
The pattern shown in the sequence 2, 6, 10, 14... is an arithmetic sequence where each term increases by 4. To generalize this pattern and find the nth term, we look for a formula that, when given a specific term number (n), will result in the value of that term in the sequence.
The correct formula for this sequence is a(n) = 2 + 4(n-1). To understand why, let's break it down. The first term is 2, which is our starting point. For each subsequent term, we add 4 more than we did for the previous term, which is an arithmetic sequence with a common difference of 4. Therefore, for the nth term, we would have added 4 to the base term (2) exactly (n-1) times.
By substituting different values of n, we can see that this formula holds true for all terms in the sequence: For n=1, a(n) = 2+4(1-1) = 2, which is the first term. For n=2, a(n) = 2+4(2-1) = 6, which is the second term, and so on.