Question

A certain species of tree grows an average of 4.2 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

Average growth rate = 4.2 cm/week.

So, common difference d = 4.2

The height of the tree a0 = 200 centimeters.

The height of the tree after end of the first week a₁ = 200 + 4.2 = 200 + 4.2(1)

The height of the tree after end of the second week a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).

The height of the tree after end of the third week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).

The height of the tree after the end of the nth week an = 200 + 4.2(n).

The equation is a_n = 200 + 4.2(n).