To solve this problem, let us break it into steps:

Step 1: Identify the common difference

The given sequence is: $13, 21, 29, 37, \dots$ We calculate the difference between consecutive terms: $21 - 13 = 8, \quad 29 - 21 = 8, \quad 37 - 29 = 8$ The common difference $d$ is 8.

Step 2: Formulate the $n$th term rule

The general formula for the $n$th term of an arithmetic sequence is: $a_n = a_1 + (n-1)d$ Here:

• $a_1 = 13$ (the first term)
• $d = 8$ (the common difference)

Substituting these values into the formula: $a_n = 13 + (n-1) \cdot 8$ Simplify: $a_n = 13 + 8n - 8$ $a_n = 8n + 5$

Step 3: Calculate the 11th term

To find the 11th term ($a_{11}$): $a_{11} = 8(11) + 5$ $a_{11} = 88 + 5 = 93$

Final Answer: The 11th term is $93$.

Would you like a detailed explanation of any step or have any additional questions?

Related Questions

1. What is the formula for the sum of the first $n$ terms of an arithmetic sequence?
2. Can you derive the 20th term of this sequence using the same formula?
3. How would the sequence change if the first term was $15$ instead of $13$?
4. How can you verify if a given number belongs to this sequence?
5. What is the difference between arithmetic and geometric sequences?

Tip: Always double-check the formula by testing it with known terms from the sequence.