Question

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?

Answer 1

Answer:

Given,

The number posts = 5,

Which are placing in ascending order,

Also, every post is $\frac{5}{6}$ of the height of the next larger post.

If the larger post has the height of 3 feet,

Then the height of second larger post =  $3\times \frac{5}{6}$

Height of third larger post =  $3\times \frac{5}{6}\times \frac{5}{6}$

Height of fourth larger post =  $3\times \frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}$

Height of fifth larger post or smallest post =  $3\times \frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}$

Which is the required expression,

By solving it,

The height of the smallest post  = $3\times \frac{625}{1296}$ = 1.45 feet ( approx )

Answer 2

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.