The given sequence is: 2, 4, 6, 8, ...

This is an arithmetic sequence, where each term increases by a common difference. Here, the difference between consecutive terms is $d = 2$.

The general formula for the $n$-th term of an arithmetic sequence is:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_1 = 2$ (the first term),
• $d = 2$ (the common difference),
• $n$ is the position of the term.

Using this, the $n$-th term for your sequence becomes:

$a_n = 2 + (n - 1) \cdot 2 = 2n$

Thus, the formula for the $n$-th term of the sequence is $a_n = 2n$.

Next few terms:

• 10th term: $2 \times 10 = 20$
• 20th term: $2 \times 20 = 40$

Would you like more details or have any questions?

5 Related Questions:

1. What is the sum of the first $n$ terms of this arithmetic sequence?
2. How can we derive the general term for a geometric sequence?
3. What if the common difference were negative? How would the sequence change?
4. Can you find the difference between the 50th and 30th terms?
5. How do arithmetic sequences relate to real-life scenarios?

Tip: Always double-check the common difference to ensure that a sequence is arithmetic!