The sequence in the image is:

$-18, -22, -26, -30, -34, \dots$

This sequence is an arithmetic sequence where each term is obtained by subtracting 4 from the previous term. To find the explicit formula, let's define it:

1. The first term ($a_1$) is $-18$.
2. The common difference ($d$) is $-4$.

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

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

Substituting $a_1 = -18$ and $d = -4$:

$a_n = -18 + (n - 1)(-4)$

Simplify:

$a_n = -18 - 4(n - 1)$ $a_n = -18 - 4n + 4$ $a_n = -4n - 14$

Final Explicit Formula:

$a_n = -4n - 14$

This formula gives the $n$-th term of the sequence.

Would you like more details or have any questions?

Related Questions:

1. What is the 10th term in this sequence?
2. How can we verify if a number (e.g., -50) belongs to this sequence?
3. What is the sum of the first 20 terms of this sequence?
4. How do we derive the sum formula for an arithmetic sequence?
5. Can this sequence be visualized graphically as a linear equation?

Tip:

When working with arithmetic sequences, always double-check the common difference and simplify the formula step by step!