Students visually explore geometric sequences by modeling the growth of a tree that doubles in height every year.
In this activity, students model tree growth using the sequence 2^{n}. They use the Line command to draw line segments, representing the height of a tree. The commands shown in the screenshot, draws lines from (1, 0) to (1, 2) and (2, 0) to (2, 4).
Students complete a table describing the x-value of the line, height of the tree, and the power of two for the years 2001 to 2008.Students complete a table describing the x-value of the line, height of the tree, and the power of two for the years 2001 to 2008.
Then students use the seq command to create a scatter plot the sequence 2^{n}. The first sequence, stored in L1, contains the integers 1 to 8, representing the years. The second sequence, stored in L2, contains the values of the sequence 2^{n}, representing the heights of the tree.