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To find the 19th term of an arithmetic sequence, we use the formula for the \( n \)-th term of an arithmetic sequence, which is given by:

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

Where:
- \( a_n \) is the \( n \)-th term we want to find.
- \( a_1 = 3 \) is the first term of the sequence.
- \( d = 4 \) is the common difference.
- \( n = 19 \) is the term number.

Substitute the values into the formula:

\[
a_{19} = 3 + (19 - 1) \cdot 4
\]

\[
a_{19} = 3 + 18 \cdot 4
\]

\[
a_{19} = 3 + 72
\]

\[
a_{19} = 75
\]

So, the 19th term of the arithmetic sequence is **75**.

Would you like more details or have any questions?

Here are some related questions for practice:

1. What is the formula for the sum of the first \( n \) terms of an arithmetic sequence?
2. How would you find the common difference if only the first term and another term are given?
3. How can you determine if a sequence is arithmetic or not?
4. If the first term of an arithmetic sequence is negative, how does that affect the sequence?
5. How can you find the middle term of an arithmetic sequence with an odd number of terms?

**Tip:** Always check that the common difference is consistent throughout when working with arithmetic sequences!

Find the 19th term of the arithmetic sequence whose common difference is d = 4 and whose first term is a_1 = 3.

Learn how to find the 19th term of an arithmetic sequence where the common difference is 4 and the first term is 3. This problem introduces core concepts of arithmetic sequences and is ideal for students in Grades 7-9.

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