Given the equation:

\[
a_n = 3a_1 + 4
\]

where the first term \( a_1 = 5 \), let's find the value of \( a_n \).

Substitute \( a_1 = 5 \) into the equation:

\[
a_n = 3(5) + 4
\]

Now calculate:

\[
a_n = 15 + 4 = 19
\]

So, \( a_n = 19 \).

Would you like further details, or do you have any questions?

Here are some related questions for practice:
1. What would be the value of \( a_n \) if the first term were 6?
2. How would the equation change if the constant added was 6 instead of 4?
3. What is the general form of an arithmetic sequence?
4. If \( a_n = 25 \), what would the first term be?
5. How does modifying the multiplier of \( a_1 \) affect the result?

**Tip:** Always verify the structure of the sequence or equation to ensure proper substitution.

Learn how to solve the arithmetic sequence equation a_n = 3a1 + 4, where the first term is 5. This problem explores algebraic concepts related to sequences and arithmetic progressions. Suitable for students in Grades 6-8.

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