https://file.aiquickdraw.com/mathbot/file/1737525142239vo6lg4x1.jpg

The problem in the image asks us to find the sum of the first 20 terms of the sequence \(1.5, 1.45, 1.40, 1.35, \dots\).

### Step 1: Identify the sequence type
This sequence is **arithmetic** because the difference between consecutive terms is constant:
\[
\text{Common difference, } d = 1.45 - 1.5 = -0.05.
\]

### Step 2: Formula for the sum of the first \(n\) terms of an arithmetic sequence
The sum of the first \(n\) terms is given by:
\[
S_n = \frac{n}{2} \left( 2a + (n-1)d \right),
\]
where:
- \(a\) is the first term,
- \(d\) is the common difference,
- \(n\) is the number of terms.

### Step 3: Substituting values
Here:
- \(a = 1.5\),
- \(d = -0.05\),
- \(n = 20\).

Substitute these values into the formula:
\[
S_{20} = \frac{20}{2} \left( 2(1.5) + (20-1)(-0.05) \right).
\]

Simplify step-by-step:
\[
S_{20} = 10 \left( 3 + 19(-0.05) \right),
\]
\[
S_{20} = 10 \left( 3 - 0.95 \right),
\]
\[
S_{20} = 10 \times 2.05 = 20.5.
\]

### Final Answer:
The sum of the first 20 terms is:
\[
\boxed{20.5}.
\]

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Would you like further clarification or a detailed breakdown of any step?  

### Follow-up questions to explore:
1. What is the formula for the nth term of an arithmetic sequence?
2. How do we recognize an arithmetic sequence from a list of terms?
3. What happens if the common difference is positive rather than negative?
4. How would you compute the sum if \(n\) were very large?
5. Can you derive the sum formula for arithmetic sequences from scratch?

### Tip:
When solving sequence problems, always verify the type of sequence (arithmetic, geometric, etc.) first to apply the correct formula!

Find the sum of the first 20 terms. 1.5, 1.45, 1.40, 1.35, ...

Learn how to calculate the sum of the first 20 terms of the arithmetic sequence 1.5, 1.45, 1.40, 1.35, ... using the sum formula for arithmetic sequences. Perfect for Grades 8-10 students studying sequences and series.

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