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To find the 55th term of the 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 we want to find.

### Step 1: Identify \( a_1 \) and \( d \)
From the sequence \( 8, 24, 40, \dots \):
- The first term \( a_1 = 8 \).
- The common difference \( d = 24 - 8 = 16 \).

### Step 2: Plug in values for \( n = 55 \)
We want to find the 55th term (\( a_{55} \)):

\[
a_{55} = 8 + (55 - 1) \cdot 16
\]
\[
a_{55} = 8 + 54 \cdot 16
\]
\[
a_{55} = 8 + 864
\]
\[
a_{55} = 872
\]

### Answer
The 55th term of the arithmetic sequence is **872**.

Would you like more details on any of the steps?

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Here are five related questions to deepen understanding:
1. What is the formula for the sum of the first \( n \) terms of an arithmetic sequence?
2. How do you find the common difference in an arithmetic sequence?
3. What would be the 100th term of this sequence?
4. How would you identify if a sequence is arithmetic or geometric?
5. Can a term in an arithmetic sequence be negative, and under what conditions?

**Tip:** In an arithmetic sequence, each term increases (or decreases) by the same fixed amount, known as the common difference.

Find the 55th term of the arithmetic sequence 8, 24, 40, …

Learn how to find the 55th term in the arithmetic sequence 8, 24, 40 with a detailed step-by-step solution. This problem uses the formula for the n-th term of an arithmetic sequence and covers key concepts suitable for students in Grades 9-10.

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