Question

Fill in the missing values in the Red Maple tree table.

Answer 1

The diameter of a tree grows a certain amount each year. If the tree's growth is constant, meaning that the amount the tree grows is the same each passing day, then the tree's growth can be expressed as an arithmetic sequence:

xₙ=a+d(n-1)

Where

xₙ represents the tree growth for the nth year

a is the initial diameter of the tree

d is the common difference, and represents the amount that the tree's diamenter increases each year

(n-1) represents any number in the sequence except the first one.

To determine the common difference you have to calculate the difference between any value of the sequence and the number below:

`\begin{gathered} d=4.3-4 \\ d=0.3 \end{gathered}`

This means that the increase of the diameter of the tree is 0.3 inches each year.

For the third value of the sequence (2nd year) the tree diameter is:

`4+0.3\cdot(3-1)=4.6`

And for the fifth value in the sequence (4th year) the tree diameter is

`4+0.3\cdot(5-1)=5.2`