https://file.aiquickdraw.com/mathbot/file/1730888190910h27uufim.jpg

To solve this problem, let's analyze the given information:

1. The staircase has 20 steps.
2. Each step is 5 inches higher than the previous one.
3. The first step is 8 inches high.

This is an arithmetic sequence problem where:
- The first term, \( a_1 \), is 8 inches.
- The common difference, \( d \), is 5 inches.

We need to find the height of the 20th step, which is the 20th term in this sequence.

The formula for the \( n \)-th term of an arithmetic sequence is:
\[
a_n = a_1 + (n - 1) \times d
\]

Substituting the values:
\[
a_{20} = 8 + (20 - 1) \times 5
\]
\[
a_{20} = 8 + 19 \times 5
\]
\[
a_{20} = 8 + 95
\]
\[
a_{20} = 103
\]

Thus, the height of the top (20th) step is **103 inches**.

Would you like further details or have any questions?

Here are some related questions to explore further:
1. How do we find the sum of all the heights in this staircase?
2. What if the common difference was different, say 3 inches? How would that change the height of the top step?
3. How do we calculate the total height climbed if we consider each step?
4. How does this concept of arithmetic sequences apply in real-world situations like staircases?
5. How would the problem change if the staircase had a different number of steps?

**Tip:** When dealing with arithmetic sequences, remember that the \( n \)-th term formula, \( a_n = a_1 + (n - 1) \times d \), is very useful to quickly determine any term in the sequence without listing all terms individually.

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 find the height of the top step in a staircase with 20 steps, where each step is 5 inches higher than the previous one, starting at 8 inches. This problem covers arithmetic sequences, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation