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The problem asks to find the 23rd term of an arithmetic sequence where the common difference \( d = 3 \) and the first term \( a_1 = 2 \).

The formula for the \( n \)-th term of an arithmetic sequence is given by:

\[
a_n = a_1 + (n - 1) \cdot d
\]

Substituting the known values:

\[
a_{23} = 2 + (23 - 1) \cdot 3
\]
\[
a_{23} = 2 + 22 \cdot 3
\]
\[
a_{23} = 2 + 66 = 68
\]

So, the 23rd term of the arithmetic sequence is \( a_{23} = 68 \).

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:
1. What is the general formula for the sum of the first \( n \) terms of an arithmetic sequence?
2. How do you determine the common difference if only the first and a later term are known?
3. Can you explain the relationship between arithmetic sequences and linear functions?
4. How can we derive the \( n \)-th term if only two terms of the sequence are provided?
5. What is the geometric interpretation of an arithmetic sequence?

**Tip:** Always keep track of the position (n) and the common difference when working with arithmetic sequences.

Find the 23rd term of the arithmetic sequence whose common difference is d=3 and whose first term is a_1=2.

Learn how to find the 23rd term of an arithmetic sequence where the common difference is 3 and the first term is 2. This problem covers essential arithmetic sequence concepts and is suitable for students in Grades 7-9.

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