The given sequence is: 10, 14, 18, 22.

This is an arithmetic sequence because the difference between consecutive terms is constant.

To find the general term $a_n$ of an arithmetic sequence, we use the formula:

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

Where:

• $a_1$ is the first term of the sequence,
• $d$ is the common difference between consecutive terms,
• $n$ is the term number we are looking for.

Step 1: Identify the values

• First term $a_1 = 10$
• Common difference $d = 14 - 10 = 4$

Step 2: General formula

Substitute $a_1$ and $d$ into the formula:

$a_n = 10 + (n - 1) \cdot 4$ Simplifying:

$a_n = 10 + 4n - 4$ $a_n = 4n + 6$

Step 3: Find the $n$-th term

The $n$-th term is given by the formula:

$a_n = 4n + 6$

So, for any value of $n$, you can find the corresponding term in the sequence.

Would you like further details on this? Here are five related questions to consider:

1. What is the 10th term of this sequence?
2. How do we derive the formula for an arithmetic sequence?
3. What would the sum of the first 20 terms of this sequence be?
4. How does the formula change for geometric sequences?
5. How can we determine whether a sequence is arithmetic or geometric?

Tip: In an arithmetic sequence, the common difference $d$ remains the same throughout, which simplifies predicting future terms!