IM Alg2.1.10 Lesson: Situations and Sequence Types
Here is a geometric sequence:
16, 24, 36, 54, 81 What is the growth factor?
One way to describe its growth is to say it’s growing by ____% each time. What number goes in the blank for the sequence 16, 24, 36, 54, 81? Be prepared to explain your reasoning.
The table shows two animal populations growing over time.
Are the sequences represented by Population and Population arithmetic or geometric?
Explain how you know.
Write an equation to define Population .
Write an equation to define Population .
Does Population ever overtake Population ? If so, when? Explain how you know.
Define the sequence W so that W(n) is the number of white squares in Step n, and define the sequence B so that B(n) is the number of black squares in Step n.
Are the sequences and arithmetic, geometric, or neither? Explain how you know.
Write an equation for sequence .
Write an equation for sequence .
Is the number of black squares ever larger than the number of white squares? Explain how you know.
A definition for the term of the Fibonacci sequence is surprisingly complicated. Humans have been interested in this sequence for a long time—it is named after an Italian mathematician who lived from around 1175 to 1250. The first person known to have stated the term definition, though, was Abraham de Moivre, a French mathematician who lived from 1667 to 1754. So, this definition was unknown for hundreds of years! Here it is: Which form (recursive or term) is more convenient to use for finding ?
What about ?
What about ?
What are some advantages and disadvantages of each form?