An arithmetic sequence has first term 8 and second term 16.  What is the third term?


In an arithmetic sequence, the difference between consecutive terms is constant. This difference is known as the **common difference** (\(d\)).

Given:
- First term (\(a_1\)) = 8
- Second term (\(a_2\)) = 16

The common difference is calculated as:

\[
d = a_2 - a_1 = 16 - 8 = 8
\]

Now, to find the third term (\(a_3\)), we use the formula for the \(n\)-th term of an arithmetic sequence:

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

For the third term (\(a_3\)):

\[
a_3 = a_1 + 2 \cdot d = 8 + 2 \cdot 8 = 8 + 16 = 24
\]

So, the third term is **24**.

Would you like further details or have any questions?

Here are some related questions:
1. How do you find the common difference in any arithmetic sequence?
2. What is the formula for the sum of the first \(n\) terms of an arithmetic sequence?
3. How can you determine whether a sequence is arithmetic or geometric?
4. What if the first term and the common difference are negative? How does it affect the sequence?
5. How do you derive the \(n\)-th term formula for an arithmetic sequence?

**Tip:** Always check if the difference between consecutive terms is constant when identifying an arithmetic sequence.

An arithmetic sequence has first term 8 and second term 16. What is the third term?

Learn how to find the third term in an arithmetic sequence where the first term is 8 and the second term is 16. This step-by-step solution explains key concepts like common difference and the arithmetic sequence formula, suitable for students in Grades 6-8.

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