The sequence 4, 9, 13, 18 has a pattern based on addition. Specifically, the sequence increases by a constant difference, which is 5 in this case. Here’s how it works:

1. Identify the difference: Each term is obtained by adding 5 to the previous term:

   • $9 - 4 = 5$
   • $13 - 9 = 4$
   • $18 - 13 = 5$

2. Classification: This is an arithmetic sequence, where each term after the first is formed by adding a common difference to the previous term.

3. General formula: For an arithmetic sequence with a common difference $d$ and first term $a$, the $n$-th term $T_n$ can be found using the formula: $T_n = a + (n - 1) \times d$ Here, $a = 4$ and $d = 5$. So, $T_n = 4 + (n - 1) \times 5$

Would you like more details or have any questions?

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1. What is an arithmetic sequence, and how does it differ from a geometric sequence?
2. How can you find the sum of an arithmetic sequence?
3. How can this formula be used to find, say, the 20th term in the sequence?
4. What other types of sequences exist besides arithmetic?
5. How can arithmetic sequences be applied in real-world scenarios?

Tip: To quickly recognize an arithmetic sequence, look for a consistent difference between consecutive terms.