Final answer:
The nth term of the sequence -2, 6, 14, 22, 30 is determined by the arithmetic sequence formula an = -2 + (n - 1)×8, which simplifies to the nth term 8n - 10.
Step-by-step explanation:
To determine the nth term of the given sequence, we need to identify the pattern in which the numbers are increasing. Observing the sequence -2, 6, 14, 22, 30, we see that each term is obtained by adding 8 to the previous term. This sequence is an arithmetic sequence.
To find the nth term, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term of the sequence, n is the term number, and d is the common difference between terms.
For this sequence, a1 = -2 (the first term) and d = 8 (the common difference, since we are adding 8 each time).
Plugging the values into the formula, we get:
an = -2 + (n - 1)×8 = -2 + 8n - 8 = 8n - 10
Therefore, the nth term of the sequence is 8n - 10.