Question

What linear function defines the following arithmetic sequence: -4, -1, 2, 5, 8, ...?

Answer 1

The linear function that defines the arithmetic sequence -4, -1, 2, 5, 8, ... is f(x) = -4 + (x - 1) * 3.

Step-by-step explanation:

The given arithmetic sequence is -4, -1, 2, 5, 8, ...

To find the linear function that defines this sequence, we can observe that the difference between consecutive terms is constant. In this case, the common difference is 3.

Using the formula for the nth term of an arithmetic sequence, which is given by an = a1 + (n - 1) * d,

1. where an is the nth term,
2. a1 is the first term (in this case, -4),
3. n is the position of the term,
4. and d is the common difference (in this case, 3).

Plugging in the values, we can find the linear function that defines the sequence:

1. For the first term, n = 1: a1 = -4.
2. For the second term, n = 2: a2 = -4 + (2 - 1) * 3 = -1.
3. For the third term, n = 3: a3 = -4 + (3 - 1) * 3 = 2.
4. For the fourth term, n = 4: a4 = -4 + (4 - 1) * 3 = 5.

Therefore, the linear function that defines the given arithmetic sequence is f(x) = -4 + (x - 1) * 3.