Solve for the 11th Term in Sequence: 2, 5, 8, ...

To solve this problem, we'll follow these steps:

• Step 1: Identify the rule of the sequence
• Step 2: Use the rule to find the 11th term

Now, let's work through each step:
Step 1: The given sequence starts with 2, 5, 8. We determine the pattern by finding the difference between consecutive terms:
$5 - 2 = 3$ and $8 - 5 = 3$ so the common difference ($d$) is 3.
This indicates it is an arithmetic sequence with $a_1 = 2$ and $d = 3$.

Step 2: Use the arithmetic sequence formula to find the 11th term $a_{11}$:
$a_n = a_1 + (n-1)d$
Substitute the known values:\
$a_{11} = 2 + (11-1) \cdot 3$
$a_{11} = 2 + 10 \cdot 3$
$a_{11} = 2 + 30$
$a_{11} = 32$

Therefore, the 11th element in the sequence is $32$, which corresponds to choice $32$.