The given sequence is: $3, 9, 15, 21, 27, \ldots$.

This is an arithmetic sequence, where each term increases by a constant difference. The common difference $d$ can be calculated as: $d = 9 - 3 = 6$

The general formula for the $n$-th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \times d$ where:

• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

For this sequence:

• $a_1 = 3$
• $d = 6$
• $n = 50$

Substituting these values into the formula: $a_{50} = 3 + (50 - 1) \times 6$ $a_{50} = 3 + 49 \times 6$ $a_{50} = 3 + 294 = 297$

So, the 50th term of the sequence is 297.

Would you like further details or have any questions?

Here are some related questions to explore:

1. What is the sum of the first 50 terms of this arithmetic sequence?
2. How would the formula change for a geometric sequence?
3. What is the 100th term of this sequence?
4. How do you derive the formula for the $n$-th term of an arithmetic sequence?
5. What are some real-life applications of arithmetic sequences?

Tip: Arithmetic sequences are very useful in calculating regularly spaced events, like schedules or payments.