find the 45th term of the arithmetic sequence a_n=2+4(n-1)

To find the 45th term of the arithmetic sequence given by the formula \( a_n = 2 + 4(n-1) \), we can substitute \( n = 45 \) into the formula.

### Formula for the \( n \)-th Term

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

\[
a_n = 2 + 4(n-1)
\]

### Calculating the 45th Term \( a_{45} \)

Substitute \( n = 45 \) into the formula:

\[
a_{45} = 2 + 4(45-1)
\]

Simplify inside the parentheses:

\[
a_{45} = 2 + 4 \times 44
\]

Now, perform the multiplication:

\[
4 \times 44 = 176
\]

Add this result to 2:

\[
a_{45} = 2 + 176 = 178
\]

### Conclusion

Thus, the 45th term of the arithmetic sequence is **178**.

If you have any questions or need further details, feel free to ask! Here are some questions you might consider:

1. How do you derive the formula for an arithmetic sequence?
2. What is the difference between an arithmetic sequence and a geometric sequence?
3. How can I find the sum of a certain number of terms in an arithmetic sequence?
4. How are arithmetic sequences used in real-life applications?
5. What is the effect of the common difference in an arithmetic sequence?

**Tip:** In arithmetic sequences, the common difference \( d \) represents the consistent amount added to each term to get the next term.

Learn how to find the 45th term of an arithmetic sequence using the formula a_n = 2 + 4(n-1). This problem involves arithmetic sequence concepts and calculations, suitable for Grades 7-9.

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