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.