To find the $n^{\text{th}}$ term of this arithmetic sequence, we need the following steps:

Step 1: Identify the common difference ($d$)

The terms are: $2, 8, 14, 20, 26, \ldots$

The difference between consecutive terms is: $d = 8 - 2 = 6$

This is the common difference.

Step 2: Find the first term ($a$)

The first term is: $a = 2$

Step 3: General formula for the $n^{\text{th}}$ term

The formula for the $n^{\text{th}}$ term of an arithmetic sequence is: $T_n = a + (n-1) \cdot d$

Substitute $a = 2$ and $d = 6$: $T_n = 2 + (n-1) \cdot 6$

Simplify: $T_n = 2 + 6n - 6$ $T_n = 6n - 4$

Final Answer:

The $n^{\text{th}}$ term rule is: $T_n = 6n - 4$

Would you like me to explain any part of this further or provide examples?

Related Questions:

1. How do you derive the $n^{\text{th}}$ term rule for a geometric sequence?
2. What is the difference between an arithmetic and geometric sequence?
3. How can you calculate the sum of the first $n$ terms in an arithmetic sequence?
4. What happens if the common difference ($d$) is negative in an arithmetic sequence?
5. How would you find the term number ($n$) for a given value in an arithmetic sequence?

Tip:

To confirm your $n^{\text{th}}$ term rule, substitute values of $n$ (e.g., $n=1, 2, 3$) and check if they match the sequence terms.