IM Alg2.1.6 Lesson: Representing Sequences
For each sequence shown, find either the growth factor or rate of change. Be prepared to explain your reasoning.
5, 15, 25, 35, 45, . . .
Starting at 10, each new term is less than the previous term.
for
Take turns with your partner to match a sequence with a recursive definition. It may help to first figure out if the sequence is arithmetic or geometric.
- For each match that you find, explain to your partner how you know it’s a match.
- For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
Complete the table. Drag the Sequences and Definitions to the right place.
Here is a pattern where the number of small squares increases with each new step.
Write a recursive definition for the total number of small squares in Step .
Sketch a graph of S that shows Steps 1 to 7.
Is this sequence geometric, arithmetic, or neither? Be prepared to explain how you know.
Start with a circle.
If you make 1 cut, you have 2 pieces. If you make 2 cuts, you can have a maximum of 4 pieces. If you make 3 cuts, you can have a maximum of 7 pieces.
Draw a picture to show how 3 cuts can give 7 pieces.
Find the maximum number of pieces you can get from 4 cuts.
From 5 cuts.
Can you find a function that gives the maximum number of pieces from cuts?