Final answer:
The nth term rule for the arithmetic sequence starting with 8, 10, 12, 14 is given by the formula a_n = 2n + 6.
Step-by-step explanation:
The arithmetic sequence shown starts with 8 and increases by 2 each time. To find the nth term rule for an arithmetic sequence, we use the formula a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference between the terms.
In this sequence, a_1 = 8 and d = 2. Plugging these values into the formula gives us:
a_n = 8 + (n - 1)·2
Expanding the formula we get:
a_n = 8 + 2n - 2
a_n = 2n + 6
Therefore, the nth term rule for this sequence is a_n = 2n + 6.