Question

"Arithmetic sequence:

0, 4, 8, 12

Is this an arithmetic sequence, and why or why not?

If it is, use the explicit formula above to create an equation to find the nth term.

Answer 1

The sequence 0, 4, 8, 12 is an arithmetic sequence with a common difference of 4. The nth term can be found using the formula an = 4n - 4.

Step-by-step explanation:

Yes, the sequence 0, 4, 8, 12 is indeed an arithmetic sequence. The reason it's an arithmetic sequence is because the difference between each term and the previous one is constant. In this case, each term is 4 more than the previous term.

To find the nth term of an arithmetic sequence, we use the formula an = a1 + (n - 1)d, where a1 is the first term and d is the common difference between the terms. For this sequence, a1 = 0 and d = 4. Plugging these values into the formula, we get:

an = 0 + (n - 1) × 4

Simplifying, we have:

an = 4n - 4