Final answer:
The given arithmetic sequence -7, -4, -1, ..., 290 has 100 terms. By using the formula for the nth term of an arithmetic sequence, we can calculate the number of terms by finding the point where the sequence reaches 290.
Step-by-step explanation:
To find the number of terms in the arithmetic sequence -7, -4, -1, ..., 290, we can use the formula for finding the nth term of an arithmetic sequence: a_n = a_1 + (n - 1) * d. In this case, our first term a_1 is -7 and the common difference d is 3 (because the sequence progresses by adding 3 each time: -7 + 3 = -4, -4 + 3 = -1, and so on).
We can set up the equation to solve for n:
-7 + (n - 1) * 3 = 290
Also, we need to solve for n:
-7 + 3n - 3 = 290
3n - 10 = 290
3n = 300
n = 100
Thus, there are 100 terms in the given arithmetic sequence.