The question shows a pattern of dots with the following sequence of figures and asks for an expression that represents the number of dots in figure $n$.

Observing the number of dots in each figure:

• Figure 1: 4 dots
• Figure 2: 7 dots
• Figure 3: 10 dots
• Figure 4: 13 dots

Analyzing the pattern:

The sequence of dots is 4, 7, 10, 13.
This is an arithmetic sequence, where each term increases by 3:

• $7 - 4 = 3$
• $10 - 7 = 3$
• $13 - 10 = 3$

Since it increases by a constant difference, the general formula for an arithmetic sequence is:
$a_n = a_1 + (n - 1) \times d$
where $a_1$ is the first term, and $d$ is the common difference.

Applying the values:

• $a_1 = 4$
• $d = 3$

The formula becomes:
$a_n = 4 + (n - 1) \times 3$
Simplify the expression:
$a_n = 4 + 3n - 3 = 3n + 1$

Expression for the number of dots in figure $n$:

$\boxed{3n + 1}$

Comparing with the given response:

The expression $4n - 1$ was suggested, but that does not match the sequence, since it does not correctly account for the difference of 3 between consecutive figures.

Would you like to explore more examples or need additional clarification?

5 Related Questions:

1. What would the number of dots be in figure 10 using the expression $3n + 1$?
2. How can you check if a sequence is arithmetic or geometric?
3. What is the general form of an arithmetic sequence, and how does it apply to this pattern?
4. How do we derive a formula for geometric sequences when the difference is not constant?
5. How can you visualize or predict figure 5 in the given pattern?

Tip: Always look for a constant difference in a sequence to determine if it is arithmetic, and apply the appropriate formula.