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Given the first three terms give me the formula and solutions

The image shows three terms: \( 8.1 \), \( 8.0 \), and \( 7.9 \).

These terms appear to form an arithmetic sequence (a sequence where each term is obtained by adding or subtracting a constant value to the previous term). In this case, the common difference \( d \) is:

\[
d = 8.0 - 8.1 = -0.1
\]
\[
d = 7.9 - 8.0 = -0.1
\]

So, the sequence decreases by 0.1 at each step.

### General 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 (8.1 in this case),
- \( d \) is the common difference (-0.1),
- \( n \) is the term number.

### Using this formula:
For the given terms:
- First term \( a_1 = 8.1 \)
- Second term \( a_2 = 8.1 + (2-1) \cdot (-0.1) = 8.0 \)
- Third term \( a_3 = 8.1 + (3-1) \cdot (-0.1) = 7.9 \)

This confirms the arithmetic sequence.

Would you like to see more terms or any specific solutions?

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Here are 5 relative questions to expand on this topic:
1. What happens if the common difference changes in an arithmetic sequence?
2. How would you derive the sum of the first \(n\) terms of this sequence?
3. Can you find the 10th term of the sequence?
4. How do arithmetic sequences differ from geometric sequences?
5. What is the formula for the sum of an infinite arithmetic sequence?

**Tip**: When working with arithmetic sequences, always double-check the common difference to ensure consistency between the terms.

Learn how to find the formula for an arithmetic sequence using the first three terms (8.1, 8.0, 7.9). This problem covers key algebraic concepts and provides step-by-step solutions. Suitable for Grades 7-9.

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