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.
200 200.5 201.0 ...
h(x) = 200 + 0.5x
To write an equation for the sequence representing the weekly height of the tree, we can use the formula for arithmetic sequence:
an = a1 + (n-1)d
Where:
an = the nth term in the sequence
a1 = the first term in the sequence
n = the term number
d = the common difference between consecutive terms
In this case, the first term (a1) is when the tree is 200 centimeters tall, and the common difference (d) is 0.5 cm per week.
So, the equation for the sequence representing the weekly height of the tree would be:
an = 200 + (n-1) * 0.5
This equation allows you to calculate the height of the tree at any given week by substituting the value of 'n' with the desired term number.