Question

A certain species of tree grows an average of 0.5 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 200 centimeters tall.

Answer 1

The heights of the tree form an arithmetic sequence. The first measurement is 200 cm, so the first term a₁=200. The tree grows 0.5 cm per week, so the common difference d=0.5.

$a_n=a_1+d(n-1) \\ a_n=200+0.5(n-1) \\ a_n=200+0.5n-0.5 \\ a_n=0.5n+199.5$

The equation for the weekly height is:
$\boxed{a_n=0.5n+199.5}$
where n is the number of week.