Answer:
Given,
The number posts = 5,
Which are placing in ascending order,
Also, every post is [tex]\frac{5}{6}[/tex] 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 = [tex]3\times \frac{5}{6}[/tex]
Height of third larger post = [tex]3\times \frac{5}{6}\times \frac{5}{6}[/tex]
Height of fourth larger post = [tex]3\times \frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}[/tex]
Height of fifth larger post or smallest post = [tex]3\times \frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}[/tex]
Which is the required expression,
By solving it,
The height of the smallest post = [tex]3\times \frac{625}{1296}[/tex] = 1.45 feet ( approx )
