To identify which sequences are arithmetic, let's analyze each provided sequence:

1. 0, 10, 20, 30, ...

   • Difference between consecutive terms:
     $10 - 0 = 10$, $20 - 10 = 10$, $30 - 20 = 10$.
     The common difference is 10, so this is an arithmetic sequence.

2. 3, 5, 7, 9, ...

   • Difference between consecutive terms:
     $5 - 3 = 2$, $7 - 5 = 2$, $9 - 7 = 2$.
     The common difference is 2, so this is an arithmetic sequence.

3. 4, 8, 16, 32, ...

   • Difference between consecutive terms:
     $8 - 4 = 4$, $16 - 8 = 8$, $32 - 16 = 16$.
     The differences are not consistent, so this is not an arithmetic sequence.

4. 8, 11, 13, 16, ...

   • Difference between consecutive terms:
     $11 - 8 = 3$, $13 - 11 = 2$, $16 - 13 = 3$.
     The differences are inconsistent, so this is not an arithmetic sequence.

5. 13, 29, 45, 61, ...

   • Difference between consecutive terms:
     $29 - 13 = 16$, $45 - 29 = 16$, $61 - 45 = 16$.
     The common difference is 16, so this is an arithmetic sequence.

Final Answer:

The arithmetic sequences are:

• 0, 10, 20, 30, ...
• 3, 5, 7, 9, ...
• 13, 29, 45, 61, ...

Would you like a detailed explanation of arithmetic sequences or help with related concepts?

Questions for further exploration:

1. What is the formula to find the $n$-th term of an arithmetic sequence?
2. How can we determine the sum of the first $n$ terms of an arithmetic sequence?
3. What distinguishes an arithmetic sequence from a geometric sequence?
4. How can arithmetic sequences be applied to solve real-world problems?
5. Can a sequence with variable differences ever be considered arithmetic?

Tip:

To quickly verify if a sequence is arithmetic, calculate the difference between