Final answer:
To find the nth term of the arithmetic sequence, we calculate the common difference from given terms and use it to find the first term. The nth term formula for this sequence, with a common difference of -8, is an = 14 + (n - 1)(-8).
Step-by-step explanation:
We are given that the third term of an arithmetic sequence is -2 and the fifth term is -18. In an arithmetic sequence, any term can be expressed as an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference.
To find the nth term formula for this sequence, we first need to find the common difference d. We have the information that a5 = a3 + 2d = -18 and a3 = -2. Using this information, we can find d by solving the equation -18 = -2 + 2d which gives us d = -8.
Now, using the common difference and the fact that a3 = a1 + 2d, we can solve for a1. Substituting d = -8 and a3 = -2, we get -2 = a1 + 2(-8) which simplifies to a1 = 14. Therefore, the nth term of the sequence can be expressed as an = 14 + (n - 1)(-8).