The problem asks how many dots are in the 10th pattern of a sequence. Let’s analyze the dot pattern:

1. First pattern (1st): There are 5 dots.
2. Second pattern (2nd): There are 9 dots.
3. Third pattern (3rd): There are 13 dots.

Observing the Pattern:

The number of dots increases by 4 in each successive pattern:

• $5, 9, 13, \dots$

This is an arithmetic sequence where:

• First term ($a$) = 5
• Common difference ($d$) = 4

Formula for the $n$-th term of an arithmetic sequence:

$a_n = a + (n-1) \cdot d$ Substituting:

• $a = 5$, $d = 4$, $n = 10$: $a_{10} = 5 + (10-1) \cdot 4$ $a_{10} = 5 + 36 = 41$

Answer:

The 10th pattern has 41 dots.

Would you like a detailed explanation of arithmetic sequences or other help?

Related Questions:

1. What is the formula for the total number of dots up to the $n$-th pattern?
2. How does the common difference affect the growth of the sequence?
3. What are the 4th, 5th, and 6th terms of this sequence?
4. Can you derive a general rule for patterns increasing by other common differences?
5. How do arithmetic sequences compare to geometric sequences?

Tip: Arithmetic sequences are identified by their constant difference between consecutive terms. Always check this first!