There are 5 posts supporting the guard rail for the steps to your home the tallest post is 3 feet tall the height of each of the other post is 5/6 the height of the next larger post.

write an expression what is the height of the shortest post?

The heights of the posts needed to support the house form a geometric sequence with initial value of 3 ft and r equal to 5/6. The height of the shortest post, that is the fifth post, is calculated through the equation,

h5 = a1 x (r) ^ (n - 1)

Substituting,

h5 = (3 ft) x (5/6) ^ (5-1)

h5 = 1.45 ft.