Find the 55th term of the arithmetic sequence 8, comma, 24, comma, 40, comma, point, point, .8,24,40,...

To find the 55th term of the arithmetic sequence \(8, 24, 40, \dots\), we'll follow these steps:

### Step 1: Identify the first term (\(a_1\)) and the common difference (\(d\)).
- The first term \(a_1 = 8\).
- The common difference \(d\) is calculated by subtracting the first term from the second term:

\[
d = 24 - 8 = 16
\]

### Step 2: Use the formula for the \(n\)th term of an arithmetic sequence.
The general formula for the \(n\)th term of an arithmetic sequence is:

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

### Step 3: Substitute the values to find the 55th term (\(a_{55}\)).
Here, \(n = 55\), \(a_1 = 8\), and \(d = 16\):

\[
a_{55} = 8 + (55 - 1) \times 16
\]

\[
a_{55} = 8 + 54 \times 16
\]

\[
a_{55} = 8 + 864
\]

\[
a_{55} = 872
\]

So, the 55th term of the sequence is \(872\).

Would you like to explore this further or have any questions?

Here are 5 related questions:
1. What is the sum of the first 55 terms of this sequence?
2. What would the sequence look like if the common difference were \(10\) instead of \(16\)?
3. Can you find the 100th term of this sequence?
4. How does the formula for the \(n\)th term change if the common difference is negative?
5. How do you find the arithmetic mean between two terms in an arithmetic sequence?

**Tip:** When working with arithmetic sequences, remember that the difference between consecutive terms remains constant, which makes it easy to predict future terms.

Learn how to find the 55th term of the arithmetic sequence 8, 24, 40, ... with a detailed step-by-step solution. This problem covers key concepts in arithmetic sequences, including the formula for the nth term. Suitable for students in Grades 7-9.

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