The first four terms of an arithmetic sequence are 3,10,17 and 24 what is the eighth term of this sequence.
49, 55, 59, or 52,?

To find the eighth term of an arithmetic sequence, we need to identify the common difference (\(d\)) and use the formula for the \(n\)-th term of an arithmetic sequence, which is given by:

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

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

First, let's determine the common difference (\(d\)):

\[ d = a_2 - a_1 = 10 - 3 = 7 \]

The first term (\(a_1\)) is 3. We need to find the eighth term (\(a_8\)):

\[ a_8 = a_1 + (8-1)d \]
\[ a_8 = 3 + (7 \cdot 7) \]
\[ a_8 = 3 + 49 \]
\[ a_8 = 52 \]

Thus, the eighth term of the arithmetic sequence is 52.

Would you like more details or have any questions?

Here are 5 more questions for you to ask:
1. How do you find the sum of the first \(n\) terms in an arithmetic sequence?
2. What is the formula for the \(n\)-th term of a geometric sequence?
3. How do you determine the common ratio in a geometric sequence?
4. What is the difference between an arithmetic and a geometric sequence?
5. How do you solve a system of linear equations?

**Tip:** Always double-check your calculations, especially when dealing with sequences and series, to ensure accuracy.

Learn how to find the eighth term of an arithmetic sequence starting with terms 3, 10, 17, and 24. Understand the concept of arithmetic sequences and use the formula for the nth term. Suitable for Grades 7-9 students studying sequences and series in mathematics.

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