Acertain species of tree grows an average of 3.8 cm per week. write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.

The answer is f(x) = 500 + 3.8x

The number of weeks is x. So, weekly, the tree grows 3.8x. 
If the measurements of the growth begin when the tree started to grow, the equation would be: f(x) = 3.8x.
But, the measurements begin when the tree is 5 m tall. Since 1 m is 100 cm, this means that 5 m is 500 cm. Thus, the equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall is:
f(x) = 500 + 3.8x