An arithmetic sequence is a sequence of numbers where each term increases or decreases by a fixed, constant value called the common difference ($d$).

Example:

Let’s consider an arithmetic sequence with a first term ($a$) of 3 and a common difference ($d$) of 5.

The sequence is: $3, 8, 13, 18, 23, 28, \dots$

Explanation:

1. The first term is $a = 3$.
2. The common difference is $d = 5$.
3. To generate each subsequent term, add the common difference to the previous term:
   • Second term: $3 + 5 = 8$
   • Third term: $8 + 5 = 13$
   • Fourth term: $13 + 5 = 18$, and so on.

The general formula for the $n$-th term of an arithmetic sequence is: $a_n = a + (n - 1)d$

For this sequence: $a_n = 3 + (n - 1)5$

Do you want more examples or details on how to derive this formula?

5 Related Questions:

1. How do you determine the sum of the first $n$ terms of an arithmetic sequence?
2. What happens if the common difference ($d$) is negative?
3. How can you identify if a given sequence is arithmetic?
4. What are some real-life applications of arithmetic sequences?
5. Can an arithmetic sequence have fractions or decimals?

Tip:

Always verify the common difference by subtracting consecutive terms to ensure the sequence is arithmetic.