Find the 30th term of the arithmetic sequence 8, 12, 16, 20, ….


To find the 30th term of an arithmetic sequence, we can use the formula for the \(n\)-th term of an arithmetic sequence:

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

Where:
- \(a_n\) is the \(n\)-th term
- \(a_1\) is the first term
- \(d\) is the common difference
- \(n\) is the term number

Given:
- \(a_1 = 8\)
- \(d = 12 - 8 = 4\)
- \(n = 30\)

Now, substitute the values into the formula:

\[
a_{30} = 8 + (30 - 1) \cdot 4
\]
\[
a_{30} = 8 + 29 \cdot 4
\]
\[
a_{30} = 8 + 116 = 124
\]

So, the 30th term of the sequence is **124**.

Would you like further clarification or details on this? Here are some related questions:

1. How can you find the sum of the first 30 terms of this sequence?
2. What is the formula for the sum of an arithmetic sequence?
3. How do you identify the common difference in an arithmetic sequence?
4. How do arithmetic sequences relate to linear functions?
5. Can you determine the 100th term of this sequence?

**Tip**: In an arithmetic sequence, the difference between consecutive terms remains constant, which is why it's called a "common difference."

Find the 30th term of the arithmetic sequence 8, 12, 16, 20, ….

Learn how to find the 30th term of the arithmetic sequence starting with 8, 12, 16, 20. This problem uses the nth-term formula for arithmetic sequences and is suitable for students in Grades 6-8. Step-by-step explanation included.

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