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To solve this problem, we need to determine the height of the top (20th) step, given that:

1. The first step is 8 inches high.
2. Each subsequent step is 5 inches higher than the previous one.
3. There are a total of 20 steps.

### Solution
This is an arithmetic sequence problem where:
- The first term \( a = 8 \) inches,
- The common difference \( d = 5 \) inches,
- We want the 20th term \( a_{20} \).

The formula for the \( n \)-th term of an arithmetic sequence is:
\[
a_n = a + (n - 1) \cdot d
\]

For the 20th step:
\[
a_{20} = 8 + (20 - 1) \cdot 5
\]
\[
a_{20} = 8 + 19 \cdot 5
\]
\[
a_{20} = 8 + 95
\]
\[
a_{20} = 103 \text{ inches}
\]

### Answer
The top (20th) step is 103 inches high.

Would you like further explanation or have any questions?

Here are some related questions for practice:
1. If the staircase had 30 steps, what would be the height of the top step?
2. If each step was only 3 inches higher than the previous one, how high would the 20th step be?
3. How high would the 15th step be in this sequence?
4. If the first step was 10 inches and each step increased by 4 inches, what would be the height of the 20th step?
5. What is the total height of all 20 steps combined?

**Tip:** In arithmetic sequences, knowing the first term and common difference helps in finding any term quickly using the \( n \)-th term formula.

A staircase has 20 steps. Each step is 5 inches higher than the previous one. If the first step is 8 inches high, how high is the top step?

Learn how to calculate the height of the top step in a staircase with 20 steps, where each step is 5 inches higher than the previous one, and the first step is 8 inches high. This problem involves understanding arithmetic sequences and applying the nth term formula, suitable for students in Grades 7-9.

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