Find the 50th term of the sequence 3,9,15,21,27

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.

Discover how to find the 50th term of the arithmetic sequence 3, 9, 15, 21, 27 using the arithmetic sequence formula. This problem explores arithmetic sequences, including identifying the common difference and calculating specific terms.

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