To find the first six terms of the sequence defined by $a_1 = 0$ and $a_n = a_{n-1} + 2$, we can calculate each term step-by-step:

1. Given: $a_1 = 0$
2. Recurrence Relation: $a_n = a_{n-1} + 2$

Let's compute the terms one by one:

• $a_1 = 0$
• $a_2 = a_1 + 2 = 0 + 2 = 2$
• $a_3 = a_2 + 2 = 2 + 2 = 4$
• $a_4 = a_3 + 2 = 4 + 2 = 6$
• $a_5 = a_4 + 2 = 6 + 2 = 8$
• $a_6 = a_5 + 2 = 8 + 2 = 10$

First six terms: $0, 2, 4, 6, 8, 10$

To graph this sequence, plot each term’s position $n$ on the x-axis and the value $a_n$ on the y-axis. The graph would show a linear pattern where each point is 2 units higher than the previous, indicating a steady increase.

Would you like a graph generated for this sequence?

Here are some related questions to expand on this concept:

1. What would the next term ($a_7$) in this sequence be?
2. How does this arithmetic sequence differ from a geometric sequence?
3. How can you find the general formula for the $n$-th term of this sequence?
4. What would happen to the sequence if $a_1$ was changed to a different value?
5. How could this sequence be represented as a function of $n$?

Tip: For arithmetic sequences, each term is generated by adding a constant difference to the previous term.